Kirby R. Cundiff, Ph.D., CFA, CFP®
Kirby R. Cundiff, Ph.D., CFA, CFP®
  • Видео 113
  • Просмотров 147 679
Chapter 13 Binomial Trees (Hull, 10th edition)
The binomial option pricing model values options using an iterative approach utilizing multiple periods to value options. When using a binomial model, there are only two possible outcomes with each iteration-a move up or a move down that follow a binomial tree. In the limit of an infinite number of interations it can be shown that the binomial model gives the same result as the Black-Scholes option pricing model. This lecture following the PPTs from the 2017 version of Chapter 13 Binomial Trees in Hull, Options, Futures, and Derivatives.
Просмотров: 258

Видео

Banking Failures During the Last 100 Years With a Focus on Silicon Valley Bank (SVB) at APEE 2024
Просмотров 279Месяц назад
In this presentation we discuss bank failures during the last 100 years. We analyze their causes and discuss how monetary and regulatory policy has contributed to them. We look at bank failures during the Great Depression of the 1930s, the Savings and Loan Fiasco of the 1980s and 90s and the bursting of the Housing Bubble in 2007-08. We propose regulatory and monetary policy changes that could ...
Binomial Trees on NVIDIA (NVDA) Call Options (Hull, Binomial Trees)
Просмотров 832 месяца назад
This video is a problem walk though of a simple one step binomial call option pricing model using NVDA one month call options as an example. The problem is similar to one found in the Hull, Options, Futures, and Derivatives text chapter on Binomial Trees. The binomial option pricing model values options using an iterative approach utilizing multiple periods to value options. When using a binomi...
Chapter 12 Trading Strategies Involving Options Part 2 (Hull, 10th edition)
Просмотров 3142 месяца назад
Trading Strategies Involving Options that are covered in this chapter include a bond plus option to create a principal protected note, a stock plus option, two or more options of the same type (a spread) and two or more options of different types (a combination). These strategies include portfolio insurance, covered calls, bull spreads, bear spreads, box spreads, butterfly spreads, calendar spr...
Chapter 12 Trading Strategies Involving Options Part 1 (Hull, 10th edition)
Просмотров 5792 месяца назад
Trading Strategies Involving Options that are covered in this chapter include a bond plus option to create a principal protected note, a stock plus option, two or more options of the same type (a spread) and two or more options of different types (a combination). These strategies include portfolio insurance, covered calls, bull spreads, bear spreads, box spreads, butterfly spreads, calendar spr...
Trump Media & Technology Group Corp. (DJT) Bull Spread (Hull, Trading Strategies Involving Options)
Просмотров 902 месяца назад
A bull spread is a combination of two call or put option with different strike prices. This example looks at creating a bull spread using two call options on Trump Media & Technology Group Corp. (DJT). A bull spread is a way of making money if a stock price goes up while limiting your losses if the stock price goes down. This problem is similar to problems in the Hull chapter on "Trading Strate...
Nvidia Corp (NVDA): How to make money if NVDA goes up or down (Straddle) (Hull)
Просмотров 2772 месяца назад
A straddle is a combination of a call and a put option with the same strike price. It is a volatility bet. A straddle pays off if the underlying stock (in this case NVDA) goes up or down significantly, but not if the stock remains near the strike price of the call and put. The problem is similar to problems in the Hull chapter on "Trading Strategies Involving Options."
Put-Call Parity for American Options (Hull, Properties of Stock Options)
Просмотров 1193 месяца назад
In this video I discuss the Put-Call Parity equation for American Stock options. An example of stock options for Nvidia Corp. (NVDA) is examined using option quotes from the E*TRADE platform. This topic is discussed in the Hull, Options, Futures, and Derivatives text chapter on Properties of Stock Options.
Recession 2024! (Tax Receipts) Full Size
Просмотров 2763 месяца назад
Recessions and tax receipts are highly correlated. As the economy contracts individuals and businesses make lower incomes and pay lower taxes. Tax receipts at the United States Federal and State levels peaked near the end of 2022 and have dropped by about 10% since that time period.
Dotcom Bubble 2.1 (Mag 7: NVDA and Friends, 2024)
Просмотров 3,1 тыс.3 месяца назад
In this video I compare current stock market conditions with what happened during the Dotcom bubble around 2000 and indicate a significant fall of the price of tech stocks is likely in 2024 or 2025. I look at the past performance of growth vs value stocks as well as the performance of QQQ and individual stocks such as AAPL, AMZN, MSFT, NVDA, ZM, and Sun Microsystems.
Put-Call Parity for European Options (Hull, Properties of Stock Options)
Просмотров 913 месяца назад
In this video I discuss the Put-Call Parity equation for European Stock options. An example of stock options for Vale S. A. is examined using option quotes from the E*TRADE platform. This topic is discussed in the Hull, Options, Futures, and Derivatives text chapter on Properties of Stock Options.
Chapter 11 Properties of Stock Options (Hull, 10th edition)
Просмотров 6354 месяца назад
This video is designed to follow the Power Point slides to accompany Chapter 11 Properties of Stock Options of the text Options Futures and other Derivatives by John Hull. In this video, I discuss the relationship of call and put prices relative to stock prices, strike prices, volatility of the underlying stock, interest rates, and dividends. I also discuss the upper and lower bounds for no arb...
A Short History of Bank Failures in the US During the Last 100 Years
Просмотров 1054 месяца назад
There have been three major sets of bank failures during the last 100 years. The failures during the Great Depression, the Savings and Loan Fiasco during the 1980s and 1990s, and the Mortgage Crisis around 2009 and 2010. The bank failures during the Great Depression were caused by banks investing depositors money in the stock market and the stock market crashing, the bank failures during the Mo...
A One Minute History of Inflation in the United States
Просмотров 2224 месяца назад
This video is a very brief history of inflation in the United States from 1800 to today. It includes a brief discussion of Thomas Jefferson, Alexander Hamilton, Andrew Jackson, and the first and second national banks. Richard Nixon's default on the international gold standard of the Bretton Woods Agreement and the massive inflation that followed is mentioned.
Recession 2024! (Fed Funds Rate) Full Size
Просмотров 9985 месяцев назад
Recession 2024! (Fed Funds Rate) Full Size
Leading Economic Indications, Recession 2024, and the S&P 500 (Full Size)
Просмотров 2,9 тыс.5 месяцев назад
Leading Economic Indications, Recession 2024, and the S&P 500 (Full Size)
Recession 2024 and an Inverted Yield Curve
Просмотров 8315 месяцев назад
Recession 2024 and an Inverted Yield Curve
Chapter 10 The Mechanics of Options Markets (Hull, 10th edition)
Просмотров 9516 месяцев назад
Chapter 10 The Mechanics of Options Markets (Hull, 10th edition)
Valuing Interest Rate Swaps (Hull, Swaps)
Просмотров 1757 месяцев назад
Valuing Interest Rate Swaps (Hull, Swaps)
Chapter 7 Swaps (Hull 10th edition)
Просмотров 1,3 тыс.7 месяцев назад
Chapter 7 Swaps (Hull 10th edition)
Valuing Currency Swaps (Hull, Swaps)
Просмотров 1428 месяцев назад
Valuing Currency Swaps (Hull, Swaps)
Capital Investment Decisions (Introductory Corporate Finance)
Просмотров 22911 месяцев назад
Capital Investment Decisions (Introductory Corporate Finance)
The Science and Politics of Climate Change -- Truman State University
Просмотров 176Год назад
The Science and Politics of Climate Change Truman State University
Duration and Convexity Calculations (Hull, Interest Rates)
Просмотров 285Год назад
Duration and Convexity Calculations (Hull, Interest Rates)
Chapter 6 Interest Rate Futures (Hull 10th)
Просмотров 1,2 тыс.Год назад
Chapter 6 Interest Rate Futures (Hull 10th)
Buy International: 2023 Outlook for the Stock Market and Commodities
Просмотров 221Год назад
Buy International: 2023 Outlook for the Stock Market and Commodities
Duration and Convexity Graphs and Equations (Hull, Interest Rates)
Просмотров 272Год назад
Duration and Convexity Graphs and Equations (Hull, Interest Rates)
Duration, Bond Prices, and Yields (Hull, Interest Rates)
Просмотров 278Год назад
Duration, Bond Prices, and Yields (Hull, Interest Rates)
Treasury Bond Futures (Cash and Quoted Prices) (Hull, Interest Rate Futures)
Просмотров 699Год назад
Treasury Bond Futures (Cash and Quoted Prices) (Hull, Interest Rate Futures)
Day Count Conventions for Bonds, Bills, and Money Market Instruments (Hull, Interest Rate Futures)
Просмотров 614Год назад
Day Count Conventions for Bonds, Bills, and Money Market Instruments (Hull, Interest Rate Futures)

Комментарии

  • @samuelrodriguezz
    @samuelrodriguezz 7 дней назад

    Excelent Explanation, precise and concise. Good job

  • @aborucu
    @aborucu Месяц назад

    Hello Kirby, interest rate denoted by I in discrete compunding is periodic rate not the usual simple annualized version which is the usual quotation am I correct ? forex. t=0.25 simple annual interest quotation is 0,0004 * 4 = 0,0016 = 0,16%. In Hulls book cahpter example table 4.7 they quote simple annual rates.

    • @KirbyCundiff
      @KirbyCundiff Месяц назад

      Correct, perhaps I should have used I/m.

  • @fojiyokaadda9099
    @fojiyokaadda9099 Месяц назад

    Hull, J. C., & Basu, S. (2010). Options, Futures and Other Derivatives (7th ed.).

  • @Angry_Bob
    @Angry_Bob Месяц назад

    You know what if you search for this it’s hard to find much information on it. Thanks for the upload

  • @floorgang1483
    @floorgang1483 Месяц назад

    Why so less energy? Hardly understood a thing

  • @KirbyCundiff
    @KirbyCundiff Месяц назад

    www.independent.org/pdf/working_papers/76_expectancy.pdf

  • @KirbyCundiff
    @KirbyCundiff Месяц назад

    www.utgjiu.ro/revista/ec/pdf/2012-03/1_KIRBY%20R.%20CUNDIFF.pdf

  • @kaywa8537
    @kaywa8537 Месяц назад

    Hi, thank you for these videos they are extremely well explained, will you be doing an episode on option greeks, chapter 17 I believe. Thanks

  • @john-od9sl
    @john-od9sl Месяц назад

    Thank you !

  • @angrymountainbikershow3151
    @angrymountainbikershow3151 Месяц назад

    The list at @46:21 is a who's who of discredited and rebutted scientists, most of whom have taken materially relevant amounts of financial remuneration directly from fossil fuel companies or from organizations with significant financial support from those companies. Their "science" has been rebutted independently again and again by repeated studies by indepentent research groups. I suggest your own ignorance in climate science is preventing you from making meaningful arguments, because you haven't grasped the complexity of the interconnected, interdependent environmental feedback mechanisms. You are squarely in the peak of the Dunning-Kreuger curve here, where you know enough to believe you know enough. I hope you continue research with an open mind and correct your many, many errors in this presentation, and consider removing it before in contributes more to the misinformation prevalent on this topic. Stick to options strategies and gaming the crooked markets. Science has enough mediocre talent, yours is not needed.

    • @KirbyCundiff
      @KirbyCundiff Месяц назад

      It is good to hear from you Will! I hope to see you at the class reunion this fall. Would you like to comment on any of the data presented in the video or let me know where a Ph.D. in many-body and astrophysics can sign up to get some of that oil company money you mentioned? I assume by "independent" you mean tax payer funded research groups. ;)

  • @havish6483
    @havish6483 Месяц назад

    Extremely concise and useful, thanks!

  • @john-od9sl
    @john-od9sl 2 месяца назад

    NEED CHAPTER 13 SIR !

    • @KirbyCundiff
      @KirbyCundiff 2 месяца назад

      I will work on it.

    • @john-od9sl
      @john-od9sl 2 месяца назад

      @@KirbyCundiff amazing thank you very much. I appreciate all of your work and efforts you put into the video. I have an exam for Chapter 3,5,7& 13 on Tuesday. I will be reviewing with your previous videos. Again thank you for your amazing work Dr. Cundiff

    • @KirbyCundiff
      @KirbyCundiff Месяц назад

      Done

  • @anshlakhanpal-hh1rz
    @anshlakhanpal-hh1rz 2 месяца назад

    Really helped me a lot.

  • @bunnyc1390
    @bunnyc1390 3 месяца назад

    is APV same as FCFF?

    • @KirbyCundiff
      @KirbyCundiff 3 месяца назад

      No, APV will be calculated using FCFF.

  • @kaktiswastik1183
    @kaktiswastik1183 3 месяца назад

    hello sir, I found your teaching quite helpful to understand Bootstrapping, could you please please help me understand the impacts of Bootstrapping and Risk free rate over foreign exchange rate?

    • @KirbyCundiff
      @KirbyCundiff 3 месяца назад

      ruclips.net/video/j50zzJZeKSw/видео.html

    • @KirbyCundiff
      @KirbyCundiff 3 месяца назад

      ruclips.net/video/YvRskwXh8gk/видео.html

    • @KirbyCundiff
      @KirbyCundiff 3 месяца назад

      In some cases IRP and PPP work. PPP only over the long term. In cases like Japan and China their central banks intervene a lot in exchange rates.

  • @KirbyCundiff
    @KirbyCundiff 3 месяца назад

    finance.yahoo.com/news/sec-adopts-landmark-climate-rule--heres-what-that-means-for-public-companies-172839134.html?.tsrc=fin-notif

  • @importedmusic
    @importedmusic 3 месяца назад

    "It's different this time...", good video thank you.

  • @saintgavinsitu
    @saintgavinsitu 3 месяца назад

    3:30 the graph and this guy is so misleading. The so-called "slight elevation" is actually 519, 3 times higher than 2001 peak of 154. Is this guy actually a professor? This is blatant misinformation

    • @KirbyCundiff
      @KirbyCundiff 3 месяца назад

      You are correct, I misspoke for some reason at the end of that graph. I meant to be referring to two different time periods 2000 to 2007 and Dec 2021 until today. From Dec 2021 until 2024 the S&P has only produced a total return of around 6% (total not per year) plus dividends.

    • @KirbyCundiff
      @KirbyCundiff 3 месяца назад

      seekingalpha.com/article/4536244-investing-in-another-lost-decade

  • @KirbyCundiff
    @KirbyCundiff 3 месяца назад

    thefelderreport.com/2017/10/26/what-were-you-thinking/

  • @fernendo4
    @fernendo4 3 месяца назад

    What was the pe and ps of sun at its peak??

  • @nunoalexandre6408
    @nunoalexandre6408 3 месяца назад

    Love it!!!!!!!!!!!!

  • @fernendo4
    @fernendo4 3 месяца назад

    Thank you s much for this. No one talks about Sun.

  • @mrpickle23
    @mrpickle23 3 месяца назад

    yawn.... SPX to 6k by end of June easy....

  • @bryonseverns5919
    @bryonseverns5919 3 месяца назад

    How AI takes over the world: 1. Chip stocks rise to the top. 2. Moore's law ends, so chip production must double every two years to compensate. 3. AI engineers become superior to human engineers. 4. AI designs a superior computer (for example, a quantum computer).

  • @JorgeOrpinel
    @JorgeOrpinel 3 месяца назад

    If there are all these new regulations, why are there so many reports of POORER quality homes being built, which mat end up costing more to live in and maintain?

    • @KirbyCundiff
      @KirbyCundiff 3 месяца назад

      I was told a few years ago by a city codes director that I would have to pay an architect $2k for permission to move a light switch in an office building. I could easily see how new regulations could lead to poorer quality home and agree many new homes are very poorly built.

  • @jeffjones114
    @jeffjones114 3 месяца назад

    I have to disagree with this "analysis" as it pertains to Nvidia. 1st, price to earnings is really more important than price to sales. Nvidia's business has a wide moat and a high margin as a result. 2nd, it is divorced from the outlook of the buisiness. We already know they are sold out of chips for the rest of 2024 and into 2025. Furthermore, companies will want to upgrade with their H200 chips to save on energy costs. Worst case scenario is 100 billion in earnings this year, this means a PE ratio of 40. And the industry is only growing. I agree Nvidia is not cheap, but 900 is not crazy either.

    • @gertjh5u64u
      @gertjh5u64u 3 месяца назад

      Yes, now we have a huge demand so the price is high and the margin profit is extremely high. In future margin profit should decrease to normal value and stock market price will crash. Question only when.

    • @lavenderlilacproductions
      @lavenderlilacproductions 3 месяца назад

      How will demand hold when companies have to do it with 6% money? Or if JPowell channels Volcker (PBUH) and finally cranks to 15% to kill inflation?

    • @TheFireGiver
      @TheFireGiver 3 месяца назад

      ​@lavenderlilacproductions they're already talking about decreasing interest rates since inflation is much more manageable now. No one is pushing it to 15% unless inflation goes absolutely insane again.

    • @socalboogie1099
      @socalboogie1099 3 месяца назад

      @@gertjh5u64u- That’s probably the best and only bear position on NVDA. Of course it will eventually crash, but when? It could go to $2,000 then crash to $1,000. Nobody knows? Margins will continue to remain high for the next year at least. Beyond that will hinge on continued demand and Nvidia’s success in staying ahead of the competition and innovating.

  • @schizosaint777
    @schizosaint777 4 месяца назад

    Gee thank you algorithm for this information that only makes me more angry. Good video though

  • @Calaber24p
    @Calaber24p 5 месяцев назад

    What would be your response to criticism from many people who believe the game changed during covid. Both sides have no fiscal responsibility and the massive amount of money printing to pay for infrastructure and other services, will keep the stock market propped up , at least in nominal terms ? Not to mention the ocean of money sitting in money market accounts that will seek a better return when cuts eventually do happen? Personally I'm about half and half. The labor market looks solid still, earnings are still pretty solid, P/e ratios are higher than historical averages, but access to the stock market has also never been easier. Millions can buy fractions of a share from their phone so overvaluation could be here for good. I think the fiscal irresponsibility of both parties and willingness to print more if we do go through a recession, can keep the market artificially propped up for a long time. I could see the market negative for the year, but I'm not convinced a crash is likely.

    • @KirbyCundiff
      @KirbyCundiff 5 месяцев назад

      www.federalreserve.gov/financial-stability/bank-term-funding-program.htm

    • @KirbyCundiff
      @KirbyCundiff 5 месяцев назад

      www.zerohedge.com/markets/jobs-shocker-december-payrolls-unexpectedly-surge-unemployment-rate-slides-wages-jump

    • @KirbyCundiff
      @KirbyCundiff 5 месяцев назад

      I generally don't like, this time it is different arguments. I agree with you that P/Es are not that bad by recent (very elevated) standards and government spending has a lot to do with why the market is up. The government is already bailing out the banking sector and without government hiring the jobs report would look much worse. I will bet on money markets at 5% over the S&P for the next year. Some international stocks look better. All of the government spending may be able to delay a recession until after the November elections.

  • @basicboomer519
    @basicboomer519 5 месяцев назад

    So stack cash?

  • @KirbyCundiff
    @KirbyCundiff 5 месяцев назад

    eujournal.org/index.php/esj/article/view/2332/9489

  • @deseosuho
    @deseosuho 5 месяцев назад

    The S&P was NOT a leading indicator in 08-09. That recession is now officially dated to start December 07, right around all time highs. In the last 20 years, at least, the stock market has been a coincident indicator with employment, which lags behind new orders and profits.

    • @KirbyCundiff
      @KirbyCundiff 5 месяцев назад

      Good point. The S&Ps peak was in October 2007 and the LEI was already forecasting a recession by then.

  • @Simon-ql7cx
    @Simon-ql7cx 6 месяцев назад

    Thank you for this helpful video!

  • @Kailas-ds2bc
    @Kailas-ds2bc 6 месяцев назад

    Sir can u give me formula for european 30/360 day count convention? I need to calculate days btwn 28/29 Feb to 31 Aug as 180. I m not sure what formula to use?

  • @bilimveedebiyatnizinden3152
    @bilimveedebiyatnizinden3152 7 месяцев назад

    Can you bring Turkish subtitles?

    • @KirbyCundiff
      @KirbyCundiff 7 месяцев назад

      Sorry I don't know how to do that.

    • @bilimveedebiyatnizinden3152
      @bilimveedebiyatnizinden3152 7 месяцев назад

      @@KirbyCundiff Add subtitles 1)Sign in to RUclips Studio. 2)Select Subtitles from the left side menu. 3)Click the video you want to edit. 4)Click ADD LANGUAGE and select the language you want. 5)Click ADD under subtitles.

    • @KirbyCundiff
      @KirbyCundiff 7 месяцев назад

      @@bilimveedebiyatnizinden3152 Thanks. It looks like Turkish subtitles cannot be autogenerated. I either have to type in subtitles in English and then convert them to Turkish or someone would have to send me a Turkish language file.

  • @KirbyCundiff
    @KirbyCundiff 7 месяцев назад

    seekingalpha.com/article/4645345-value-stocks-are-usually-a-safe-haven-during-bear-markets

  • @emonhossin6475
    @emonhossin6475 10 месяцев назад

    chapter ending question solving video needed

    • @KirbyCundiff
      @KirbyCundiff 7 месяцев назад

      There are several chapter ending questions: look for (Hull, Interest Rates) in video title.

  • @hihi-dt3sq
    @hihi-dt3sq 10 месяцев назад

    Hello, how do you find Rm and unlevered firm’s beta

    • @randymi9334
      @randymi9334 6 месяцев назад

      Those are arbitrarily chosen constants here

  • @kaiwang2924
    @kaiwang2924 Год назад

    Thanks for the wonderful videos! They are very practical, not only text books.

  • @acidleviathan994
    @acidleviathan994 Год назад

    great series mate, cheers

  • @stts762
    @stts762 Год назад

    Something doesn't look right to me with the time value It's increasing up to 50 and than it drops off So the ITM option has no time value ?

    • @KirbyCundiff
      @KirbyCundiff Год назад

      For an option, the time value should peak when a stock is at the money. I believe this table and graph is correct.

    • @stts762
      @stts762 Год назад

      @@KirbyCundiff You are correct I guess I was thinking it would be similar to an expiration line but it is not

  • @markbaugh6083
    @markbaugh6083 Год назад

    Thank you for your video. Some of the charts are very blurry. Clicking ‘higher picture quality’ doesn’t seem to increase their readability.

    • @KirbyCundiff
      @KirbyCundiff Год назад

      It looks like I only uploaded the video in 480p. Sorry, that was the first time I used new video recording software.

  • @Simon-fw1qi
    @Simon-fw1qi Год назад

    Im so confused by the rsL and rsU. Unlevered cost of capital should equal cost of equity, and therefore use the CAPM equation. Levered cost of capital means that there is debt in the Cap structure and therefore should be using the WACC formula. Yet this video swops this around. Can someone please explain?

  • @dhirajmeenavilli5508
    @dhirajmeenavilli5508 Год назад

    Are futures and other hedging tools available/reasonable for retail investment use or is it purely for corporations. Thanks

    • @KirbyCundiff
      @KirbyCundiff Год назад

      Futures and options are available for trading through most online brokerages. For hedging purposes derivatives are useful. As investing products for the retail investor, I would only recommend selling covered calls or selling puts on stocks you are thinking about buying.

    • @dhirajmeenavilli5508
      @dhirajmeenavilli5508 Год назад

      @@KirbyCundiff Thank you.

  • @Expertinexcel1
    @Expertinexcel1 Год назад

    Thank you. I have 2 questions. 1: what rate you used to find Horizon values and why? 2: why you used rsU for discounting explicit tax shield? Will we not use rsL since, there will be debt and shareholders will require debt risk adjusted return (levered beta with CAPM). Please answer.

  • @leonardopaez3242
    @leonardopaez3242 Год назад

    You explain this better than my professor. Thank you!!

  • @Kig_Ama
    @Kig_Ama Год назад

    Where can I download the file?

    • @KirbyCundiff
      @KirbyCundiff Год назад

      I can share it with you if you want to become a consulting client.

    • @Kig_Ama
      @Kig_Ama Год назад

      @@KirbyCundiff oh I am just a random guy from germany interested in stock markets, was asking getting it for free.

  • @Kig_Ama
    @Kig_Ama Год назад

    Where can I get the sheet?

  • @joshfump8238
    @joshfump8238 Год назад

    Good video. Is it your opinion that there are no real opportunities for arbitrage profit after all costs are input with formula?

    • @KirbyCundiff
      @KirbyCundiff Год назад

      Thank you! My guess is it would depend on the market. Since computers running trading programs looking for arbitrages are watching most liquid large markets, it is unlikely you will find any arbitrages there. The computers might make small arbitrage profits. In smaller less active markets arbitrages are more likely.

  • @menonguy
    @menonguy Год назад

    can you tell us from which chapter is this from?

    • @KirbyCundiff
      @KirbyCundiff Год назад

      Interest Rate Futures which is chapter 6 in the 10th edition