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A stock price is currently $40. The risk-free interest rate is 12% per annum with continuous compounding. Annual continuously compounded volatility is 10%. Construct a binomial tree for two periods and calculate the value of the options by working back through the binomial tree. a) What is your replicating portfolio today for a 6-month European put option with a strike price of $42?

User Bryony
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Answer:

The replicating portfolio today for a 6-month European put option with a strike price of $42 is 0.2044

Step-by-step explanation:

Since the strike price and maturity of the options and is was not explained, I am taking these equal to that mentioned in part (a)

Kindly find an attached image showing he two step binomial tree for valuing a 1 year European put with strike, K = $42

The first step to take is to find the replicating portfolio.

Part (a): Replicating portfolio

Thus,

we calculate the delta of the put option.

We see that as the stock price changes from $40 to $44.2068, the option price changes from $0.86 to $0.00

Thus, the delta of the put option is (0-0.86)/(44.2068-40) = - 0.2044

Therefore, replicating portfolio for the 6 month European put option with K=$42 is selling short 0.2044 shares for each contract and lending cash for 6 months at the risk free rate.

A stock price is currently $40. The risk-free interest rate is 12% per annum with-example-1
User Rasheena
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