Binomial Option Pricing Model Flashcards
What does the Binomial Option Pricing Model represent?
It represents possible paths that the stock price might follow over the life of the option using a binomial filtration tree.
What are the key steps in the binomial approach to option pricing?
- Draw a lattice of share prices.
- Calculate the option payoffs at each node.
- Discount the expected option payoffs at the risk-free rate to find the option price.
How does risk-neutral valuation apply to option pricing?
Risk-neutral valuation assumes that investors are indifferent to risk. Option prices are calculated using the expected payoff discounted at the risk-free rate.
What is the assumption in the one-period binomial model?
The stock price can either move up by a factor u or down by a factor d in one period.
What is the purpose of creating a risk-free asset in the model?
To ensure no arbitrage, the risk-free asset must pay out the same amount in one period, regardless of whether the stock price goes up or down.
How are option payoffs determined in the binomial model?
Option payoffs are calculated as the value of the option (e.g., \max(S-K, 0) for calls) at the final nodes of the binomial tree.
How does the two-period model differ from the one-period model?
The stock price evolves over two steps, with the possible outcomes calculated iteratively based on up and down movements.
What is delta in the context of the binomial model?
Delta is the ratio of the change in the option’s price to the change in the underlying stock’s price, used to hedge risk.
How are American options priced differently from European options in the binomial model?
For American options, you test each node to determine whether early exercise is optimal, whereas European options are only exercised at expiration.
How is the N-period binomial model constructed?
By iterating the stock price movements over multiple periods and discounting payoffs back to the present value at the risk-free rate.
In a two-step example, how do you calculate the price of a European call option?
- Build the price lattice.
- Compute the payoff at expiration.
- Discount back to the present value using the risk-free rate and risk-neutral probabilities.
How are risk-neutral probabilities calculated?
p =((1+r)-d)/(u-d) where r is the risk-free rate, and u and d are the up and down factors.
What is unique about valuing American put options in the binomial model?
The option is evaluated at each node to decide whether early exercise provides more value than holding the option.
