problem 1: Describe how you would hedge a short position in a European (plain vanilla) call with six weeks to maturity if the spot price is 60, the strike is 65 and σ = 0.3, r = 0.1. You rehedge every week. Suppose that the stock will follow the given path for the end-of-week prices: 63, 59, 64, 68, 64, 67. Describe how your hedging position modifies every week and what trades you must put in to do so. Suppose there are no transaction costs. Find out the hedging cost?

problem 2: The given prices are observed in the market for an option: (all options are on the same underlying with similar maturity time).

A) Stock trades at S0 = 100. 
B) A straddle with K = 100 trades at 7.9. 
C) A strip with K = 100 trades at 12.1. 
D) A strap with K = 100 trades at 11.6. 
E) A strangle with K1 = 95 and K2 = 105 trades at 5.0. 
F) A butterfly spread with K1 = 95, K = 100 and K2 = 105 trades at 2.1.

Describe a risk-free strategy to make money in this market (just trading the above instruments)

problem 3: The European asset-or-nothing option that expired at time T pays its holder the asset value S(T) at time T is S(T) > K and pays 0 or else. Find out the no-arbitrage cost of such an option as a function of parameters s, T, K, r, σ. Find out its Delta.

problem 4: You buy 1000 six months ATM call options on the non-dividend paying asset with spot price 100, following a lognormal proves with volatility 30%. Suppose that the interest rates are constant at 5%.

A) How much do you pay for the options?
B) What Delta-hedging position do you have to take?
C) One the next trading day, the asset opens at 98. Determine the value of your position (the option and shares position)?
D) Had you not Delta-hedged, how much would you have lost due to the reduction in the price of asset?