In a 6-month European style up-and-outcalloption on a non-dividend-paying stock, the strike price is $9 and the barrier $11. The current stock price $10, the volatility is 20% p.a., and the risk-free rate is 5%p.a. Find the option price using a 2-step trinomial tree
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- Based on the put - call parity, please briefly explain how to replicate a call option of a stock with a strike price of $100. Assume that the risk-free rate is 5%.1) Draw the binomial tree listing only the option prices at each node. Assume the following data on a 6-month call option, using 3-month intervals as the time period. K = $40, S = $37.90, r = 5.0%, σ = 0.35 2) Draw the binomial tree listing only the stock prices at each node. Assume the following data on a 6-month call option, using 3-month intervals as the time period. K = $70, S = $68.50, r = 6.0%, σ = 0.32 3) Draw the binomial tree listing only the option prices at each node. Assume the following data on a 6-month put option, using 3-month intervals as the time period. K = $40.00, S = $37.90, r = 5.0%, σ = 0.35 4) Using a binomial tree explanation, explain the situation in which an American option would alter the pricing of an option.The following information is given about an Option on a stock: S(0)=$31, X=$34, rf=9%, variance (sigma squared)=20%, T=182.5 days, Dividend $1.75 in 45 days (1) Calculate the price of a European put option using the Black-Scholes pricing model (show all workings including d1, d2, N(d1), N(d2)) (2) Calculate the price of the corresponding European call option (hint: put call parity) (3) Suppose you feel that the put option is overpriced. What strategy should you use to exploit the apparent mispricing? (4) The market has entered a state of significant volatility, and you believe the implied volatility is incorrect. You believe it should be 10% higher. What trade would you undertake to exploit this arbitrage
- Assume the price of an non-dividend stock is $40, the annual volatility of the stock is 20%, and the continuous compound risk-free interest rate is 5%. What's the price of a European put option on this stock with delivery price of $40 with 1-year expiration? (The standard normal distribution table is in the attachment or you can use excel function NORMSDIST, and please keep the results with 3 decimal places.) (BS Model-Option Pricing)Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is 6 months. (a) Calculate u, d, and p for a two-step tree. (b) Value the option using a two-step tree.Consider shorting a call option c on a stock S where S = 24 is the value of the stock, K = 30 is the strike price, T = ½ is the expiration date, r = 0.04 is the continuously compounded interest rate per year, and = 0.3 is the volatility of the price of the stock. Determine the delta ratio Δ .
- Consider a European call option on a non-dividend-paying stock where the stock price is $33, the strike price is $36, the risk-free rate is 6% per annum, the volatility is 25% per annum and the time to maturity is 6 months. (a) Calculate u and d for a one-step binomial tree. (b) Value the option using a non arbitrage argument. (c) Assume that the option is a put instead of a call. Value the option using the risk neutral approach. (d) Verify that the European call and European put prices found in (b) and (c) satisfy the put-call parity.Consider an American put option (K=$100) expiring in one year on a stock trading for $84. The return volatility on the stock is 27.3% and the riskless rate is 5%. Find the price of the option using a Binomial Model with two steps. (Respond with two decimal places, such as "-12.34") 26.59 Correct Answer: 18.284. Consider a stock with a current price of S0 = $60. The value of the stock at time t = 1 can take one of two values: S1,u = $100, S1,d = $40. The price of a risk-free bond that pays out $1 in period t = 1 is $0.90. (a) Using a one-step binomial tree, write down the possible payoffs of a put option on stock S with strike K = $60 and maturity t = 1. (b) What is the price of this put option? (c) What is the price of a call option with strike K = $60 and maturity t = 1? Please use put-call parity to find the call price.
- Use the Black-Scholes formula to find the value of a call option based on the following inputs. (Round your final answer to 2 decimal places. Do not round intermediate calculations.) Stock price Exercise price Interest rate Dividend yield Time to expiration Standard deviation of stock's returns Call value GA $ $ $ 48 60 0.07 0.04 0.50 0.26Consider a stock with a current price of P = $27.Suppose that over the next 6 months the stockprice will either go up by a factor of 1.41 or downby a factor of 0.71. Consider a call option on thestock with a strike price of $25 that expires in6 months. The risk-free rate is 6%.(1) Using the binomial model, what are the endingvalues of the stock price? What are the payoffsof the call option?Please answer both questions