Using the risk-neutral probability (pi), what is the formula for the expected value of the option at expiration?
Explanation
The expected value is the probability-weighted sum of all possible outcomes.
Other questions
What is the primary assumption regarding asset price movements in a one-period binomial model?
In the context of the binomial model provided, how is the downtick factor (d) typically related to the uptick factor (u)?
Which formula correctly represents the risk-neutral probability of an upward movement?
If the risk-free rate is 5 percent, the up factor (u) is 1.2, and the down factor (d) is 0.9, what is the risk-neutral probability of an up move?
What defines a 'risk-neutral' investor?
How is the hedge ratio (h) calculated in the one-period binomial model?
In the provided example, if the Call value up (Cu) is 45 and Call value down (Cd) is 0, while Stock up (Su) is 125 and Stock down (Sd) is 80, what is the hedge ratio?
Why is the risk-neutral probability used in valuation even if investors are risk-averse?
What is the value of a call option at the 'up' node if the stock price is 110 and the strike price is 100?
When are the prices of European and American call options on the same asset typically equal?
Under what scenario is early exercise of an American Put option potentially useful?
If Stock Price (S) = 50 and Strike Price (X) = 45, what is the intrinsic value of the Call Option?
Calculate the stock price at the 'up' node if the current price is 200 and the up factor is 1.1.
If the risk-free rate is 10 percent, what is the discount factor used to value the option in a one-period model?
Which investor type would select an investment with a lower expected return if it offered significantly less risk?
What is the lower bound of a European call option's value?
In the binomial model example provided, what does the term 'U - D' represent in the probability formula?
If a stock is currently 100, u is 1.25, and d is 0.8, what is the stock price in the 'down' state?
Calculate the hedge ratio if the option payoffs are 10 (up) and 0 (down), and stock prices are 110 (up) and 90 (down).
What does a hedge ratio of 1 imply?
If the risk-free rate increases, what happens to the risk-neutral probability of an up move (holding u and d constant)?
Which option allows exercise on specific dates, such as once a month?
In the example, the calculation 45 * 66.67 percent / (1 + 0.1) yields approximately what value?
If a stock pays a significant dividend, which option might be exercised early?
In the binomial tree, what is the 'Cd' term if the strike is 80 and the down stock price is 80?
What does a risk-neutral probability of 66.67 percent represent in the provided example?
If u = 1.25, what implies that d = 0.8?
What is the value of a derivative today in the binomial model?
Calculate the risk-neutral probability if RFR is 2 percent, u is 1.1, and d is 0.95.
Which investor type is indifferent between receiving $50 for certain or a lottery with an expected value of $50?
In the binomial model, what role does the clearinghouse play?
What is the intrinsic value of a Put option at expiration if Strike (X) = 50 and Stock (S) = 40?
If a call option hedge ratio is 0.6, what does this mean for a portfolio manager?
Can the risk-neutral probability be greater than 1?
If u = 1.1 and d = 0.9, what is the risk-neutral probability if RFR = 0 percent?
Why is 'AO = EO' (American Option = European Option) for non-dividend paying calls?
What variable is NOT required to calculate the risk-neutral probability in the one-period model?
If the stock price is 100, Strike is 100, u is 1.25, and d is 0.8, what is the Call option payoff in the 'down' state?
What is the expected stock price at expiration in the risk-neutral world?
How does the binomial model account for volatility?
In a one-period binomial model, if the Hedge Ratio is 0.5 and the stock rises by $2, how much does the option value change?
What happens to the value of a call option if the volatility (spread between u and d) increases?
If calculating the value of a Put option using the binomial model, what changes in the calculation compared to a Call?
What is the key advantage of the binomial model over simple historical average pricing?
If a risk-seeking investor values the option, how would their personal valuation compare to the risk-neutral valuation?
Which factor effectively sets the 'probabilities' in the binomial pricing formula?
If the calculated Call Value Up (Cu) is 10 and Call Value Down (Cd) is 10, what is the Hedge Ratio?
Why might an analyst use a one-period binomial model despite its simplicity?
Given: S=100, u=1.2, d=0.9, RFR=5 percent. Calculate the value of a Call with Strike=100.