Question

Assume that put options on a particular stock are very thinly traded and have very high...

Assume that put options on a particular stock are very thinly traded and have very high transaction costs with a large bid-ask spread.

You desire to sell a 3-month out option on this particular stock (sell to open) but want to avoid the high transactions cost. you understand put-call parity. Assume that we are referring to European style options

A) using the principles of put call parity, how could you create a "short synthetic put" by transacting the stock, the comparable European-style call option, and risk free bond? make sure to state your answers in words in terms of what your transactions would be and be as specific as possible.

B) assume you set up the "synthetic put" Above. Then assume that the 3 month pass and the option reaches expiration. what is the payoff at option expiration of this "synthetic put"if the stock price ends less than the exercise price of the put? how does this compare to the future payoff at option expiration of an actual short put position under the same stock price outcome?

Homework Answers

Answer #1

Part (A)

Recall call put parity equation:

C - P = S - PV (K) where K is the strike price

Hence, short put position = - P = S - C - PV (K)

Hence, synthetic short put position can be created as:

  • Buy (Long) the underlying stock
  • Short (Sell) the call option of 3 months matuirity and strike price of K on the same underlying stock
  • Borrow present value of strike price today (at risk free rate over three months maturity)

Part (B)

S < K on expiration

Hence, the payoff from the synthetic position on maturity = S - C - K = S - max (S - K, 0) - K = S - K

Payoff from an actual short put position = - max (K - S, 0) = - (K - S) = S - K

Hence, the two payoffs are identical.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Imagine that you are unable to short-sell a particular stock. Using put-call parity, replicate a short...
Imagine that you are unable to short-sell a particular stock. Using put-call parity, replicate a short position in the stock, assuming that the stock pays no dividends, there is a put and a call option, both of which have the same exercise price, K, and the same time to expiration, T. You are able to borrow and lend the continuously compounded risk free rate, r.
The prices of European call and put options on a non-dividend-paying stock with 12 months to...
The prices of European call and put options on a non-dividend-paying stock with 12 months to maturity, a strike price of $120, and an expiration date in 12 months are $25 and $5, respectively. The current stock price is $135. What is the implied risk-free rate? Draw a diagram showing the variation of an investor’s profit and loss with the terminal stock price for a portfolio consisting of One share and a short position in one call option Two shares...
You purchase 100 put options on a stock with exercise price of $52 at a premium...
You purchase 100 put options on a stock with exercise price of $52 at a premium of $4.30 per put. You also purchase 100 call options on the same stock with exercise price of $54 and call premium of $5.10 per call. If at expiration of the options (the options expire on the same date), the stock's price is $52.79, calculate your profit. According to put-call parity, the present value of the exercise price is equal to the: A. Stock...
1. Tucker Inc. common stock currently trades for $90/share. 6-month European put options on the stock...
1. Tucker Inc. common stock currently trades for $90/share. 6-month European put options on the stock have an exercise price and premium of $93 and $4, respectively. The annual risk free rate is 2%. What should be the value of a 6-month European call option on the stock with an exercise price of $93 according to put-call parity? Round intermediate steps to four decimals and your final answer to two decimals. a. 7.90 b. 0.065 c. 1.93 d. 2.84 e....
Suppose that a 6-month European call A option on a stock with a strike price of...
Suppose that a 6-month European call A option on a stock with a strike price of $75 costs $5 and is held until maturity, and 6-month European call B option on a stock with a strike price of $80 costs $3 and is held until maturity. The underlying stock price is $73 with a volatility of 15%. Risk-free interest rates (all maturities) are 10% per annum with continuous compounding. Use put-call parity to explain how would you construct a European...
Part A) Using options on an asset you don’t own is called: A) speculation. B) a...
Part A) Using options on an asset you don’t own is called: A) speculation. B) a naked position. C) hedging. D) a covered position. Part B) You are short both a put option and a call option on Rockwood stock with the same expiration date. The exercise price of the call option is $40 and the exercise price of the put option is also $40. Graph the payoff of the combination of options at expiration.
Assume that the stock price is $56, call option price is $9, the put option price...
Assume that the stock price is $56, call option price is $9, the put option price is $5, risk-free rate is 5%, the maturity of both options is 1 year , and the strike price of both options is 58. An investor can __the put option, ___the call option, ___the stock, and ______ to explore the arbitrage opportunity. sell, buy, short-sell, lend buy, sell, buy, lend sell, buy, short-sell, borrow buy, sell, buy, borrow
A call option with 1 month to expiration currently sells for $0.70. A put option with...
A call option with 1 month to expiration currently sells for $0.70. A put option with the same expiration sells for $1.10. The options are European style. The risk-free rate is 3 percent per year and the strike price of both options is $17.50. What is the current stock price? Select one: a. $17.06 b. $17.63 c. $17.29 d. $17.86 e. $16.87
Use the following stock and set of options to answer #1, # 2, and #3 below....
Use the following stock and set of options to answer #1, # 2, and #3 below. A stock, priced at $47.00, has 3-month call and put options with exercise prices of $45 and $50. The current market prices of these options are given by the following: Exercise Price Call Put 45 $4.50 $2.20 50 $2.15 $4.80 1.   Assume that you feel that it is likely that the stock price will move up only very modestly over the next 3 months....
A strap option strategy is created by purchasing two call options and one put option of...
A strap option strategy is created by purchasing two call options and one put option of the same underlying stock. The options have the same exercise price (E=50) and same expiration date. a) What is the payoff of the strategy is the stock price is $0? c) What is the payoff of the strategy is the stock price is $100?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT