Can you please solve the attached 4 problems that are very similar to the ones we did before with just different numbers by using the same models. I only had difficulties with four questions, the rest 6 problems were fine.

Thank you!-

On March 2, a Treasury bill expiring on April 20 had a bid discount of 5.80, and an ask discount of 5.86. What is the best estimate of the risk-free rate as given in the text? Answer: 6.11 % Start date End date Difference Bid discount Ask discount Discount (mid-point) Discount rate TB Face Value Discount amount Price of TB Yield 2-Mar-15 20-Apr-15 49 ...days to maturity 5.80 5.86 5.83 5.83% 100 $0.79 ...Face value x Midpoint discount rate x (days to maturity / 360) $99.21 ... Face value - discount amount. 6.11% ...(Face value/Price)^(365/days to maturity)-1 The stock price was 113.25. The risk-free rates were 7.30 percent (November), 7.50 percent (December) and 7.62 percent (January). The times to expiration were 0.0384 (November), 0.1342 (December), and 0.211 (January). Assume no dividends unless indicated. Puts Calls Strike Nov Dec Jan Nov Dec Jan 105 8.4 10 11.5 5.3 1.3 2 110 4.4 7.1 8.3 0.9 2.5 3.8 115 1.5 3.9 5.3 2.8 4.8 4.8 What is the intrinsic value of the December 115 put? Answer: 1.75 Stock price Strike price Intrinsic value 113.25 115.00 1.75 ...Max(Strike price - Share price,0) Consider a binomial world in which the current stock price of 80 can either go up by 10 percent or down by 8 percent. The risk-free rate is 4 percent. Assume a one-period world. Answer questions 12 through 15 about a call with an exercise price of 80. What is the theoretical value of the call? Answer: 5.15 Inputs S u d r X 80 current stock price 1.1 up magnitude 0.92 down magnitude 0.04 risk free rate 80 strike price Calculations p 1-p 0.67 ...risk neutral probability measure. This is the risk neutral probability of a share price going up. 0.33 p = (1 + r - d)/(u - d) The Stock Price Path Time 0 Time 1 88.00 uS 80.00 73.60 dS The Call Price Path Time 0 Time 1 8.00 Max(0,Su - X) = Cu 5.15 - Max(0,Sd - X) = Cd Call price = {Cu x p + Cd x (1-p)}/(1 + r) A stock priced at 50 can go up or down by 10 percent over two periods. The risk-free rate is 4 percent. Which of the following is the correct price of an American put with an exercise price of 55? Answer: 5.00 The intrinsic value of the American put, now, is: 5 ...Max(Strike - Share price,0) If the holder of the put decides to delay exercising the put until time 2, the expected present value of the future payoff is: 3.34 The put should thus be valued at its current intrinsic value since it is optimal to exercise it now. Thus, price of American put is: 5 Inputs S u d r X 50 current stock price 1.1 up magnitude 0.9 down magnitude 0.04 risk free rate 55 strike price Calculations p 0.70 ...risk neutral probability measure. This is the risk neutral probability of a share price going up. 1-p 0.30 p = (1 + r - d)/(u - d) The Stock Price Path Time 0 Time 1 Time 2 60.50 uuS 55.00 uS 50.00 49.50 udS 45.00 dS 40.50 ddS The Put Price Path if Put is Exercised at Time 2 Time 0 Time 1 Time 2 1.59 3.34 5.50 7.88 14.50 The following information is given about options on the stock of a certain company S0 = 23 X = 20 rc = 0.09 T = 0.5 2 = 0.15 What value does the Black-Scholes-Merton model predict for the call? (Due to differences in rounding your calculations may be slightly different. \"none of the above\" should be selected only if your answer is different by more than 10 cents.) Answer: 4.73 Inputs S X T r Stdev Output Data Present Value of Exercise Price (PV(EX)) s*t^.5 d1 d2 Delta N(d1) Normal Cumulative Density Function Bank Loan N(d2)*PV(EX) Value of Call 23 20 0.5 0.09 0.387298 19.12 0.27 0.81 0.54 0.79 13.47 4.73 The following information is given about options on the stock of a certain company S0 = 23 X = 20 rc = 0.09 T = 0.5 2 = 0.15 If we now assume that the stock pays a dividend at a known constant rate of 3.5 percent, what stock price should we use in the model? (Due to differences in rounding your calculations may be slightly different. \"none of the above\" should be selected only if your answer is different by more than 10 cents.) Answer: 22.60 Current price Dividend yield T Stock price to use in model 23 3.50% 0.5 22.60 = current price x exp(-dividend yield x time) Consider a stock priced at $30 with a standard deviation of 0.3. The risk-free rate is 0.05. There are put and call options available at exercise prices of 30 and a time to expiration of six months. The calls are priced at $2.89 and the puts cost $2.15. There are no dividends on the stock and the options are European. Assume that all transactions consist of 100 shares or one contract (100 options). What is the breakeven stock price at expiration $27? Answer: $27.11 Break-even price = Strike price + call premium = 32.89 Note that at expiry, the intrisic value of the call option = Max(32.89-30) = 2.89. This is sufficient to cover the premium paid to buy the call. Answer is $28.21. Below is proof that at this price, the net profit is zero. Exercise price Call premium Stock price at expiration Current stock price 31 2.79 27 31 28.21 Payoff from writing the call option Share price at expiration Call premium Intrinsic value of call (from writer's perspective) Payoff from writing call 28.21