What is the rho of a European put option with the following parameters? As a reminder, rho is defined as the first derivative of the option price with respect to the risk free rate. s0 = $40k = $39 r = 10%sigma = 20%T = 0.75 years (required precision 0.01 +/- 0.01)   Greeks Reference Guide: Delta = ∂π/∂S Theta = ∂π/∂t Gamma = (∂2π)/(∂S2) Vega = ∂π/∂σ Rho = ∂π/∂r

Consider the following data (interest rate is per period): S = 100; K = 75;R = 1.20 ; u = 1.5 ; d = .5. 1. What is the binomial price of a European call option with two periods until expiration? What is the price an American option with the same strike price and same time to expiration. Is there ever early exercise? 2. Show that the binomial option price for a European put option with two periods to go until expiration is 3.125. Show that the binomial price for an American put is 6.25. Can you conclude from the difference in prices alone that early exercise may be optimal? When is it optimal? 3. Use your answers to (i) and (ii) to verify that put-call parity holds for European options, but not for American options. Explain all answers in detail or step by step solution.

What is the implied volatility of a European call option with the following parameters? c = $3 s0 = $40 k = 41 r = 10% T = 0.5 years (Enter 11.51% as 0.1151. Required precision +/- 0.0002)

Consider a European call option struck "at-the-money", meaning the strike price equals current stock price. There is one year until expiration and the risk-free annual interest rate is r = 0.06. We define the call option's "delta" as aCE(S,t) A as Is it possible to determine whether or not the call option's delta is greater than or less than 0.5?