1. Assume the Black-Scholes framework. The continuously compounded risk-free int

The risk free rate calculated using the formulae d1=ln[S(0)X]+(r+1/22)T/T is 20.58%.

ID: 2709733 • Letter: 1

Question

1. Assume the Black-Scholes framework. The continuously compounded

risk-free interest rate is r is unknown, but for a non-dividend paying

stock S we know:

• The current stock price S0 = 10

• The stocks volatility is 10%.

• The price of a 6-month European gap call option on S, with a

strike price of K1 = 10 and a payment trigger of K2 = 9.90, is 1.

• The price of a 6-month European gap put option on S, with a

strike price of K1 = 10 and a payment trigger of K2 = 9:90, is

0.50.

The definition of the payoffs is then

GGapCall(S) = (S - K1)1{S > K2}

GGapPut(S) = (K1 - S)1{S < K2}

Calculate r.

The risk free rate calculated using the formulae d1=ln[S(0)X]+(r+1/22)T/T is 20.58%.

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