A strangle is to hold a long European put at strike K1 and a long European call

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Question:

A strangle is to hold a long European put at strike K1 and a long European call
at strike K2, where S is the underlying and K1 < S < K2. Assume that the underlying
stock has a price of 100, an expected yearly return of μ = 7% and a volatility of
35%. The (continuously compounded) risk-free rate is given by r = 1%. The time to
maturity is one year.

a) How can you replicate the payoff using only in-the-money options, the stock
and the money market account?

b) What is the price of the strangle in the Black-Scholes-Merton model if K1 = 80
and K2 = 120?

c) How should you chose the strikes K1 and K2 if you would like the price of the
strangle to be $9.25 and still require that both K1 and K2 have the same
distance to S (the distance of K1 and K2 to S in (b) was 20)?

d) Note: If you need values for any other parameters to answer the questions
below, make reasonable assumptions and justify these. Simulate the return
distribution of the strangle if it is held until maturity. Use 1,000 simulation runs.
What is the probability that you loose all your investment with this strategy?

e) Simulate the return distribution of the strangle if it is held for only 6 months.
Again, use 1,000 simulation runs. What is the probability of loosing more than
50% after 6 months?