Consider a 3-month put (European) on a stock with K = $20. Over the next 3...

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Consider a 3-month put (European) on a stock with K = $20. Over the next 3 months the stock is expected to either rise by 10% or drop by 10%. The risk-free rate is 5%. Current stock price is 20. a. What is the risk-neutral probability of the up-move? p e'T -d u-d 0.05×1/4 -0.9 = 0.5629 1.1-0.9 b. What position in the stock is necessary to hedge a long position in 1 put option (assume no dividends)? A = Pu-Pa 0-2 = = = -0.5 S₁-Sa 22-18 c. What is the value of the put? (p=0.86) d. Assume now that the put has 6 months to maturity and there are 2 periods on the tree (each period is 3-months long). Everything else is the same. i) Compute the value of the put option. P₁ = 0.08633, Pa = 1.7515, p = 0.8041 Pu Consider a 3-month put (European) on a stock with K = $20. Over the next 3 months the stock is expected to either rise by 10% or drop by 10%. The risk-free rate is 5%. Current stock price is 20. a. What is the risk-neutral probability of the up-move? p e'T -d u-d 0.05×1/4 -0.9 = 0.5629 1.1-0.9 b. What position in the stock is necessary to hedge a long position in 1 put option (assume no dividends)? A = Pu-Pa 0-2 = = = -0.5 S₁-Sa 22-18 c. What is the value of the put? (p=0.86) d. Assume now that the put has 6 months to maturity and there are 2 periods on the tree (each period is 3-months long). Everything else is the same. i) Compute the value of the put option. P₁ = 0.08633, Pa = 1.7515, p = 0.8041 Pu