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- I asked this question yesterday: Suppose that, in each period, the cost of a security either goes up by a factor of 2 or goes down by a factor of 1/2 (i.e. u=2, d=1/2). If the initial price of the security is 100, determine the no-arbitrage cost of a call option to purchase the security at the end of two periods for a price of 150. In the answer I got today the first step said: "We assume that the probability of moving up and moving down be 50% each, which means equal chances for both the movements. " I had learned that the risk neutral probability for the stock price to go up is: p=(1+r-d)/(u-d). In this particular problem, we'd have p=(1+0-.5)/(2-.5)=1/3. And so the probability going down would be 1-p or 2/3. Thus, my question is why weren't these probabilities used in the solution previously sent? And if they should be, what would be the new solution to the problem? Thank you for your help. I'm new to learning all of this and some of it is hard for me to understand.1. Suppose that, in each period, the cost of a security either goes up by a factor of u = 2 or down by a factor d = 1/2. Assume the initial price of the security is $100 and that the interest rate r is 0. c) Assuming the strike price of a European call option on this security is $90, compute the possible payoffs of the call option given that the option expires in two periods.The prices of a certain security follow a geometric Brownian motion with parameters mu=.12 and sigma=.24. If the security's price is presently 40, what is the probability that a call option, having four months until its expiration time and with a strike price of K=42, will be exercised? (A security whose price at the time of expiration of a call option is above the strike price is said to finish in the money.) If the interest rate is 8%, what is the risk-neutral valuation of the call option?
- The prices of a certain security follow a geometric Brownian motion with parameters mu=.12 and sigma=.24. If the security's price is presently 40, what is the probability that a call option, having four months until its expiration time and with a strike price of K=42, will be exercised? (A security whose price at the time of expiration of a call option is above the strike price is said to finish in the money).Assume that K=61, St =65, t = 0.25 (i.e. time to expiry is 3 months), and the risk-free rate is 0.04. The current price of the put option is p = 4. What would the price of the call option ‘c’ need to be for put-call parity to hold?The price of a certain security follows a geometric Brownian motion with drift parameter mu=.05 and volatility parameter sigma =.3. The present price of the security is 95. (a) If the interest rate is 4%, find the no-arbitrage cost of a call option that expires in three months and has exercise price 100. (b) What is the probability that the call option in part (a) is worthless at the time of expiration?
- Assume a security follows a geometric Brownian motion with volatility parameter = 0.2. Assume the initial price of the security is 21 and the interest rate is 0. It is known that the price of a down-and-in barrier option and a down-and-out barrier option with strike price 19 and expiration 30 days have equal risk-neutral prices. Compute this common risk-neutral price.Consider a one-period model with N = {1,2,3} and two risky assets S1, S2 whose with current prices are 71 = 42 and 12 = 23 respectively. At time one, the price of S1 is believed to be either 44, 43, or 40 while the price of S2 is believed to be either 27, 22, or 20. Suppose that the risk-free interest rate is 3%. What is the unique risk-neutral probability measure Q in this situation? Select one: О а. Q(1) — 0.35, Q(2) — 0.27, Q(3) — 0.38 O b. Q(1) = 0.63, Q(2) = 0.34, Q(3) = 0.03 Ос. Q(1) — 0.25, Q(2) — 0.62, Q(3) — 0.13 O d. Q(1) = 0.35, Q(2) = 0.62, Q(3) = 0.03Assume a security follows a geometric Brownian motion with volatility parameter sigma=0.2. Assume the initial price of the security is $25 and the interest rate is 0. It is known that the price of a down-and-in barrier option and a down-and-out barrier option with strike price $22 and expiration 30 days have equal risk-neutral prices. Compute this common risk-neutral price. (I attempted this problem and got a final answer of $1.50. Not sure if that is right.)
- Assume that K=61, St =65, t = 0.25 (i.e. time to expiry is 3 months), and the risk-free rate is 0.04. The current price of the put option is p = 4. If the price of the call option is 7.17, describe the arbitrage that would be possible, and calculate the profit that would result.Calculate the implied volatility on a security given the following information: a call option on the security has a premium of 3.5p, the security itself is trading at 50p, the call has an exercise price of 51p and has 120 days to maturity, and the riskless interest rate is 12 per cent. Calculate the implied volatility on a security given the following information: a call option on the security has a premium of 3.5p, the security itself is trading at 50p, the call has an exercise price of 51p and has 120 days to maturity, and the riskless interest rate is 12 per cent.Assume a security follows a geometric Brownian motion with volatility parameter sigma=0.2. Assume the initial price of the security is $25 and the interest rate is 0. It is known that the price of a down-and-in barrier option and a down-and-out barrier option with strike price $22 and expiration 30 days have equal risk-neutral prices. Compute this common risk-neutral price. I was able to do this problem, but have a question about the interpretation of my answer. I got an answer of $3.00 for the cost of the call option, but how do I answer "compute this common risk-neutral price"? Do I have to divide the answer my 2 for each of the barrier options and say the answer is $1.50? Or because of the fact that it says common does that mean to take the combined value of $1.50+$1.50 to get $3.00 as the answer? I'm just not sure if my answer to the question is $3.00 or $1.50. Does it all depend on the word "common"? Thanks for some clarification.