Suppose put prices are given by
Strike 50 55
Put Premium 7 14
1. What no arbitrage property is violated? What spread position would you use to effect arbitrage? Demonstrate that spread position is an arbitrage by creating a table, which shows possible profit opportunities at the time to maturity. Assume option’s time to maturity is 1 year and continuously compounded interest rate is 4%.
Suppose call prices are given by
Strike 80 100 105
Call Premium 22 9 5
2. Find the convexity violations. What spread would you use the effect arbitrage? Demonstrate that spread position is an arbitrage by creating a table, which shows possible profit opportunities at the time to maturity. Assume option’s time to maturity in 1 year and continuously compounded interest rate is 4%.
3. Let S=$40, K=$40, σ=30%, risk-free interest rate, r=8% (continuously compounding), and T=0.5 year, and n=2, two-period binomial tree.
a) Construct the binomial tree for the stock. What are u and d values?
b) Compute the price of European call option.
c) Compute the prices of European put option.
d) At time 0, now, assume you write the European call option and form the replicating portfolio to offset the written option. Let’s assume that market price of this call option that you have written is $5. What is the replicating portfolio and what are the net cash flow from selling the call option and buying the synthetic equivalent?