Question

Based on the put-call parity relationship you want to make an arbitrage profit by selling a...

Based on the put-call parity relationship you want to make an arbitrage profit by selling a call, buying a put, and taking a leveraged equity position.

Stock proce = $100
Call price (6-month maturity with strike price of $110) = $5
Put price (6-month maturity with strike price of $110) = $8
Risk free interest rate (continuously compounded) = 10%

If the stock price at maturity is $120, how much do you earn from all these positions?

Homework Answers

Answer #1

Steps for given Arbitrage Strategy:

Today,

1) Borrow Amount (Stock Price+Put Premium-Call Premium) = 100+8-5 = $103 for 6 months @10%

2) Buy Stock for $100

3) Buy Put for $8

4) Sell Call for $5

Balance = 103-100-8+5 = 0

After 6 months,

Case 1: If Stock Price is less than $110, then Exercise Put and Lapse Call. Stock will be sold for $110 under Put contract.

Case 2: If Stock Price is greater than $110, then Exercise Call and Lapse Put. Stock will be sold for $110 under Call contract.

Case 3: If Stock Price is equal to $110, then Both Lapse. Stock will be sold for $110 in Market

Therefore, In any Case, we will be able to sell the stock for $110

5) Sell Stock under Call contract for $110

6) Repay loan with interest = 103*e^(0.1/2) = 103*e^0.05 = 103*1.0513(from table) = $108.28

Balance = Arbitrage Gain = 110-108.28 = $1.72

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
It has been observed that the put-call parity relation is often violated in practice – that...
It has been observed that the put-call parity relation is often violated in practice – that is, Put price > Synthetic put price = Call price + Present value of strike price –Underlying stock price + Present value of dividends. In other words, if one buys the synthetic put by buying call, buying a risk-less bond that pays the strike price at the maturity, and short-selling the underlying stock and sells the put with the same strike price as the...
a) It has been observed that the put-call parity relation is often violated in practice –...
a) It has been observed that the put-call parity relation is often violated in practice – that is, Put price > Synthetic put price = Call price + Present value of strike price – Underlying stock price + Present value of dividends. In other words, if one buys the synthetic put by buying call, buying a risk-less bond that pays the strike price at the maturity, and short-selling the underlying stock and sells the put with the same strike price...
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 current stock price is $129 and put price is $6. The risk-free interest rate is...
The current stock price is $129 and put price is $6. The risk-free interest rate is 10% per annum continuously compounded. Using the put-call parity, calculate the call price. The strike is $105 and the maturity is 0.5 year for both put and call.
~~~In Excel~~~ Question 2. 1-month call and put price for European options at strike 108 are...
~~~In Excel~~~ Question 2. 1-month call and put price for European options at strike 108 are 0.29 and 1.70, respectively. Prevailing short-term interest rate is 2% per year. a. Find current price of the stock using the put-call parity. b. Suppose another set of call and put options on the same stock at strike price of 106.5 is selling for 0.71 and 0.23, respectively. Is there any arbitrage opportunity at 106.5 strike price? Answer this by finding the amount of...
a) A stock currently sells for $33.75. A 6-month call option with a strike price of...
a) A stock currently sells for $33.75. A 6-month call option with a strike price of $33 has a premium of $5.3. Let the continuously compounded risk-free rate be 6%. What is the price of the associated 6-month put option with the same strike (to the nearest penny)?    Price = $ ------------------- b) A stock currently sells for $34.3. A 6-month call option with a strike price of $30.9 has a premium of $2.11, and a 6-month put with...
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...
Put Call Parity Using the Apple (AAPL) option chain, the stock price is $226.82, the term...
Put Call Parity Using the Apple (AAPL) option chain, the stock price is $226.82, the term is 45 days, estimate a risk-free rate (T-bill), use the 225 strike, use the bid/ ask mean quote call = $10.175. Using Put Call Parity solve for the put and please show all you work.
Question 1. Given the price of a stock is $21, the maturity time is 6 months,...
Question 1. Given the price of a stock is $21, the maturity time is 6 months, the strike price is $20 and the price of European call is $4.50, assuming risk-free rate of interest is 3% per year continuously compounded, calculate the price of the European put option? Hint: Use put-call parity relationship. Note: Bull spreads are used when the investor believes that the price of stock will increase. A bull spread on calls consists of going long in a...
You are observing the following market prices. A put option that expires in six months with...
You are observing the following market prices. A put option that expires in six months with an exercise price of $45 sells for $5.80. The stock is currently priced at $40, and the risk-free rate is 3.6% per year, compounded continuously. What is the price of a call option with the same exercise prices and maturity? In the above example, suppose you form a portfolio consisting of selling a call option and buying a put option on the same stock....