Find the price of an American call option on a futures if the current spot price is 30, the exercise price is 25, the futures price is 33.70, the risk-free interest rate is 6 percent, the spot asset can go up by 10 percent or down by 8 percent per period and the call expires in two periods, which is also when the futures expires. Show your working. A. 9.98 B. 8.70 C. 7.73 D. 8.22
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Find the price of an American call option on a futures if the current spot price is 30, the
exercise price is 25, the futures price is 33.70, the risk-free interest rate is 6 percent, the
spot asset can go up by 10 percent or down by 8 percent per period and the call expires in
two periods, which is also when the futures expires. Show your working.
A. 9.98
B. 8.70
C. 7.73
D. 8.22
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- Q roshu Suppose that a futures price is currently $42. A European call option and a European put option on the futures with a strike price of $40 and maturity in two months are both priced at $3 and $2 respectively in the market. The continuously compounded risk-free rate of interest is 5% per annum. Use the put-call parity condition to show that an arbitrage opportunity exists. Explain what position could be set up to exploit it. (Show all relevant calculations to support your argument. For example, your calculations should include what strategy an arbitrageur could follow in order to lock in a risk-free profit from the arbitrage strategy, as well as the arbitrageur’s net profit from the strategy).?Q.19 Consider a European call option with the following parameters: Assuming a risk-free annual rate of 8%, what is the probability that the option will be exercised in a risk- neutral world? (If required, use the table at the beginning of the document for statistical calculations.) Strike price USD 48 Expiration 6 months Underlying's Price USD 50 Annual volatility 25% A B C 0.70 0.5761 0.6443 D 0.3668Using put-call parity, if the price of an At-the-Money Call option maturing in 1 day is $3.14, what is the price of an of an At-the-Money Put option maturing in 1 day (give an approximation)? A. $0.95 B. $2.86 C. $3.14 D.$3.26
- You use a forward binominal tree to price options on a futures contract. You are given: i) The period is 1 year ii) The volatility of the futures price is 30% iii) The initial futures price is 100 iv) The continuously compounded risk-free rate is 3% Calculate the price of a one-year 110-strike European call option on the futures contract. A. 8.68 B 9.13 C 10.32 D 11.54 E 12.06Consider a European call option struck "at-the-money", meaning the strike price equals current stock price. There is one year until expiration and the risk-free annual interest rate is r = 0.06. We define the call option's "delta" as aCE(S,t) A as Is it possible to determine whether or not the call option's delta is greater than or less than 0.5?Suppose the following for European options: Stock price $94 3-month call options with strike price $97 3-month put option with strike price $98 1-year risk-free rate is 3%. The put option is trading ot $5 and there is an identical call option that is trading for $4. The arbitrage gain that can be made is equal to: O a. $2.00 b. $0.27 Oc. $3.00 O d. $1.27 O e $227
- Consider a European Call Option with a strike of 82. The current price of the underlying asset is 80, and the time to expiry is 5 months. The current market price of the option is 6.22. The risk-free rate is 4.1%. (a) Find the implied volatility of the underlying. Provide all necessary calculations.Question #2: Futures Contracts The chart below shows a quote for a futures contract on the NASDAQ 100 Index Delivery Date Futures Price NASDAQ 100 November 2020 9325.75 (a) This futures contract is an example of a(n) contract. Circle yŅır answer. No explanation is required Financial Futures Commodity Futures Interest Rate Futures Currency Futures (b) Assume that for the NASDAQ Futures contract the futures price is multiplied by a multiple of $100 to get the total contract value. If the margin requirement is 7%, how much must you deposit into your margin account to purchase three (3) November 2020 NASDAQ contracts? (c) Suppose the day after you purchased the 3 contracts, the NASDAQ 100 Index rises to 9400. What will happen to your margin account? (d) Suppose the NASDAQ 100 Index futures price rises by 5%. What is the percentage return on your investment on the 3 futures contracts?Consider the following data (interest rate is per period): S = 100; K = 75;R = 1.20 ; u = 1.5 ; d = .5. 1. What is the binomial price of a European call option with two periods until expiration? What is the price an American option with the same strike price and same time to expiration. Is there ever early exercise? 2. Show that the binomial option price for a European put option with two periods to go until expiration is 3.125. Show that the binomial price for an American put is 6.25. Can you conclude from the difference in prices alone that early exercise may be optimal? When is it optimal? 3. Use your answers to (i) and (ii) to verify that put-call parity holds for European options, but not for American options. Explain all answers in detail or step by step solution.
- 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 $90, compute the possible payoffs of the call option given that the option expires in two periods.Consider a European call option on a (non-dividend paying) stock currently worth £60. The option’s exercise price is £40, the continuously compounded interest rate is 2% and the option has 6 months to maturity. Which of the values below provides the tightest valid lower bound on the value of the option (rounded to the nearest penny)? Question 7Answer a. £0.00 b. £20.40 c. £20.00 d. £19.60A Eurodollar futures price changes from 99.45 to 94.32. What is the gain or loss to an investor who is long 5 contracts? Choose the right answer: a. The investor makes gain – 128.25$ b. The investor makes loss – 641.25$ c. The investor makes loss – 195$ d. The investor makes gain – 195.25$ e. The investor makes loss – 128.25$