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- 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.7) Consider a European call option on a -dividend-paying stock where the stock price is $40, the strıke price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is six months. A dividend of $1 is expected in 3 months' time a. Calculate u, d̟ and p for a two-step tree b. Value the option using a two-step tree. c. Value the option with 5 time steps using DerivaGem software.Suppose that a call option with a strike price of $48 expires in one year and has a current market price of $5.17. The market price of the underlying stock is $46.25, and the risk-free rate is 1%. Use put-call parity to calculate the price of a put option on the same underlying stock with a strike of $48 and an expiration of one year. The price of a put option on the same underlying stock with a strike of $48 and an expiration of one year is $. (Round to the nearest cent.)
- You are evaluating a put option based on the following information: P = Ke-H•N(-d,) – S-N(-d,) Stock price, So Exercise price, k = RM 11 = RM 10 = 0.10 Maturity, T= 90 days = 0.25 Standard deviation, o = 0.5 Interest rate, r Calculate the fair value of the put based on Black-Scholes pricing model. Cumulative normal distribution table is provided at the back.Consider a portfolio that consists of the following four derivatives: 1) a put option written(sold) with strike price K − 5, 2) a call option purchased with strike price K − 5, 3) a call option written(sold) with strike price K + 5, and 4) a put option purchased at strike price K + 5. All options are European.The risk-free rate is rf , the time to expiration is T, the initial stock price is S0, and the stock price atmaturity is ST . What are the payoffs at expiration of this portfolio? What must the price of this portfoliobe?Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset … what is the value of the call option?
- Assume that the value of a call option using the Black-Scholes model is $8.94. The interest rate is 8 percent, and the time to maturity is 90 days. The price of the underlying stock is $47.38, and the exercise price is $45. Calculate the price of a put using the put-call parity relationship.Consider a European call on Amazon Stock (AMZN) that expires in one period. The current stock price is $100, the strike price is $120, and the risk-free rate is 5%. Assume AMZN stock will either go up to $140 or down to $80. Construct a replicating portfolio using shares of AMZN stock and a position in a risk-free asset ... what is the value of the call option? Call Option Price = $4.84 Call Option Price = $2.95 Call Option Price = $7.93 Call Option Price = $12.04Assume 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.
- In a financial market a stock is traded with a current price of 50. Next period the price of the stock can either go up with 30 per cent or go down with 25 per cent. Risk-free debt is available with an interest rate of 8 per cent. Also traded are European options on the stock with an exercise price of 45 and a time to maturity of 1, i.e. they mature next period. Calculate the price of a call option by constructing and pricing a replicating portfolio.Suppose you want to price an American style put option for a stock being traded on theDryfontein Stock Exchange having the following parameters: s = 18, t = 0.25, K = 20, σ =0.2 and r = 0.07. Using n = 5, calculate the value of V2(2). Provide all necessary details.Let S = $100, K = $95, \sigma = 30%, r = 8%, T = 1, and \delta = 0. For simplicity, let u = 1.3, d = 0.8 and n = 2 (that is, 2 periods). When constructing the binomial tree for the European call option, what is A (Stock Share Purchased in the replicating portfolio) at the first node (Time 0)? Question 11 options: 0.1789 0.3886 1.0000 0.2550 0.6912