CFA Level I Derivatives - Binomial Model for Pricing Options

PrepNuggets
16 Jan 202005:31

Summary

TLDRThis video explains how the binomial model is used to estimate the future price of an asset, like a stock, and how this model can be applied to value options. The binomial model assumes two possible outcomes for a stock's price: an up move and a down move. By calculating the probabilities of these moves, analysts can estimate future stock prices and option payoffs. The video walks through a practical example using a stock priced at $50 and explains how to calculate the value of a call option using risk-neutral probabilities and discounting methods.

Takeaways

  • 📈 The binomial model is used to estimate the future value of an asset by considering two possible outcomes: an up move or a down move.
  • 💲 To construct a binomial model, you need the initial asset value, the up and down move sizes, and the probabilities of each move.
  • 📊 In the example, a stock priced at $50 has an up move factor of 1.25 and a down move factor of 0.8.
  • 🎲 The analyst estimates the probability of an up move at 0.6 and a down move at 0.4.
  • 📉 The expected stock price after one year is calculated as $53.50 by multiplying the potential prices with their respective probabilities.
  • 📐 The size of the up move is often based on the stock's volatility, while the probabilities are based on risk-neutral pseudo probabilities.
  • 🔢 The pseudo probability of an up move is calculated using the risk-free rate, in this case, 7%, yielding a probability of 0.6 for the up move.
  • 💼 Binomial models can be used to value options by estimating future asset prices and option payoffs in different scenarios.
  • 📅 The process for valuing a call option involves calculating the payoff at maturity, the expected option value, and discounting it to the present.
  • 💰 In the example, the value of a one-year call option with an exercise price of $45 is calculated to be $9.81.

Q & A

  • What is the basic premise of the binomial model in financial analysis?

    -The binomial model is based on the idea that the value of an asset will change to one of two possible values in the next period: one for an upward move and one for a downward move.

  • What information is required to construct a binomial model?

    -To construct a binomial model, you need to know the beginning asset value, the size of the up and down moves, and the probabilities of each move occurring.

  • In the provided example, what are the up and down factors for the stock priced at $50?

    -The up factor (U) is 1.25, indicating a 25% increase, and the down factor (D) is 0.8, which is the reciprocal of the up factor.

  • How are the probabilities of up and down moves estimated in this example?

    -The probability of an up move is estimated at 0.6, and since the events are not mutually exclusive, the probability of a down move is 0.4.

  • What is the expected stock price after one year, based on the given probabilities?

    -The expected stock price after one year is $53.50, calculated by multiplying the up and down prices by their respective probabilities and summing the results.

  • How does an analyst estimate the size of an up move?

    -The size of an up move is often estimated based on the volatility of the stock.

  • What is a risk-neutral pseudo-probability in the binomial model?

    -The risk-neutral pseudo-probability is a probability calculated based on the size of the moves and the risk-free rate. It is not the actual probability but is used for pricing options in a risk-neutral framework.

  • How do you calculate the risk-neutral pseudo-probabilities for an up move and down move?

    -Using the given formula, the risk-neutral pseudo-probability of an up move (π_U) and a down move (π_D) can be calculated. In this example, π_U is 0.6, and π_D is 0.4.

  • What are the three steps for valuing an option using the binomial model?

    -The steps are: 1) Calculate the payoff of the option at maturity for both up and down moves, 2) Calculate the expected value of the option one year from now using the pseudo-probabilities, and 3) Discount the expected value back to today using the risk-free rate.

  • What is the value of a one-year call option with an exercise price of $45, given the example data?

    -The value of the one-year call option is $9.81, calculated using the binomial pricing approach.

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Binomial ModelOption PricingStock EstimationRisk-NeutralCall OptionProbabilitiesFinanceStock MarketInvestmentQuantitative Methods
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