Q1. OPTION PRICING; THE VALUE OF INSURANCE
Assume spot gold is selling for $1,200 per ounce. Over the next period it will either rise by 10% or fall by 10%. The interest rate over the period is 5%.
A. What is the value of a European call on gold with a strike price of $1050? What is the hedge ratio?
B. Redo A. When the price of gold can either rise by 20% or fall by 10%. other things being equal, how do you account for any change, or lack of it, in the value of the call option? What is the hedge ratio?
C. Redo A. When the price of gold can either rise by 20% or fall by 20%, other things being equal, how do you account for any change. or lack of it, in the value of the call option? What is the hedge ratio?
D. What will the prices of puts be in A. B. C.?
Q2. RISK MANAGEMENT (The Greeks) - POST MODULE
In this problem set you will compute and examine the behavior of options sensitivities (the Greeks). The relevant parameters are: The underlying commodity is Gold. The volatility of the ROR on gold is 30%, time to maturity is 90 days, the 90-day risk free rate is 3% per year.
Using the B-S-M model compute the following:
a. Compute Price. Delta, Gamma, Vega and Theta, for calls and puts for the following gold prices:
i. 1160
ii. 1180
iii. 1200
iv. 1220
v. 1240 Assume the same strike (K=1200).
b. Compute Price, Delta, Gamma, Vega and Theta, for calls and puts. for the following times to expiration:
i. 30
ii. 60
iii. 90
iv. 120
v. 150
(K = 1200, S = 1200)
What have you learned from this exercise?