The stock price of Google is $32. The price of an American call option with strike price $32 and a six-month expiration date is $5 and the price of the corresponding Amertican put option (same maturity and expiration date) is $6. The risk-free interest rate is 5%. Are these prices compatible with the absence of arbitrage opportunities? Why? OI. No, because the put-call parity relationship suggests that ct - Pt = St - K exp(-RO (T-t)) and this is not satisfied in this case. O II. Yes, because the price of the American put option is greater than the price of the American call option violating the inequality conditions defining the put-call parity relationship. O II. No, because the put-call parity relationship for American options suggests that St-Ks t - Pt s St -K exp(-Ro (T-t). O IV. It depends on whether the stock pays dividends or not.

Using the Black-Scholes-Merton model, calculate the value of an European call option under the following parameters: The underlying stock's current market price is $30; the exercise price is $35; the time to expiry is 4 months; the standard deviation is 0.5; and the risk free rate of return is 5%. Group of answer choices $1.91 Cannot be determined from the given information. $3.91 $2.91

3. Consider a one-period binomial model with h = 1, S = 100, r = 0.08, u = 1.5, d = 0.8 and 8 = 0. Calculate the price of an American put option on this stock with strike price K = 100. Does early exercise occur?

What is the gamma of a European call option with the following parameters? As a reminder, gamma is defined as the first derivative of delta with respect to the stock price, or alternatively as the second derivative of the option price with respect to the stock price. s0 = $40k = $40 r = 10%sigma = 20%T = 0.75 years In order to avoid precision issues with Excel, please use an epsilon of 0.0001. (required precision 0.0001 +/- 0.0002)   Greeks Reference Guide: Delta = ∂π/∂S Theta = ∂π/∂t Gamma = (∂2π)/(∂S2) Vega = ∂π/∂σ Rho = ∂π/∂r