Problem 1. Consider a one period binomial model. Suppose $S_0 = 1$ at $t = T_0$; and $S_u = 2$ and $S_d = rac{1}{2}$ at time $T_1$. If we assume the risk free rate $R$ is 1.2, compute the current value of a European put with strike $K = 1$. Please round your answer to 2 decimals. Give your answer in % rounded to 2 decimal places. Problem 2. Compute the number of units of stock we need to short in order to replicate the option in the previous question. Please round your answer to 2 decimals.
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First, we need to calculate the risk-neutral probabilities. The risk-neutral probability of an up-move (p) is given by the formula: p = (R - d) / (u - d) where R is the risk-free rate, u is the up-move factor, and d is the down-move factor. Substituting Show more…
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Akash M.
2. Consider the case of a simple one-period framework. If i = 12.50%, k = 14.85%, p = 0.98, and g = 0.85, what is the required risk premium (rounded to two decimals)? 3. Assume that B = $200,000, r = 1 year, i = 7%, d = 0.9, N(h1) = 0.174120, and N(h2) = 0.793323. Using Moody's KMV Credit Monitor model, what is the required risk premium on the loan (rounded to two decimal places)? 4. Assume that i1 = 11% and i2 = 12%, and that k1 = 14.50% and k2 = 16.50%. What is the expected probability of repayment on the one-year corporate bonds in one year's time (rounded to two decimals)?
Adi S.
Consider the value of a European put option with a strike price of $110 and an expiration date of 6 months. The underlying stock has a current price of $100, binomial lattice parameters for a period of 1 month of u = 1.04 and d = 1/u. The risk-free interest rate is 12% per year, compounded monthly. a. Show calculations of d, R, and q below. b. Without using a spreadsheet, give the formula for P below and its numerical value. c. Determine the current value of the put option using a spreadsheet (Excel). Circle your answer for the value of the put option and write it here:
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