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Consider a European put option on a non-dividend paying stock with a strike price $52 and expiration in 8 months. The current stock price is $50. The stock's volatility is 15%. Over each of the next two 4-month periods the stock price is expected to go up by 9% or down by 8%. The risk-free interest rate is 6% per annum with continuous compounding for all maturities.
(a) Use a two-step binomial tree to calculate the value of this European put option. Show your step-by-step workings. No need to draw a binomial tree in the answer field. Just show your calculations.
(b) Use the Black-Scholes-Merton model to calculate the value of this European put option. Show your step-by-step workings.
(c) Compare the results obtained in (a) and (b). Do you expect them to be identical? Why/why not?
(d) If this option is an American option rather than a European option (all else staying the same), briefly describe how you will value this option (no calculations needed) and why.
(e) What is the Black-Scholes-Merton delta of this European put option?
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