Question

In: Finance

A stock price is $74, and current risk free interest rates are 2%. If the put...

A stock price is $74, and current risk free interest rates are 2%. If the put option with a $100 strike price expires in 6 months, and the call option is trading at $26.25, how would you arb this option?

Expert Solution

Stock current price = $74

Put option Strike price = $100

Expiry = 6 months

Risk-free rate = 2%

Risk free rate for 6 months = 2%*6/12 = 1% or 0.01

Call option price = $26.25

Present value of E.P. = E.P./(1+i)

= 100/(1+0.01)

= 99.009900990099

Theoritical Call option price = Current market price - P.V. of Exercise price

= 74 - 99.0099

= -25.01

Call option theoritical price is -$25.01. while actual price is $26.25. So Call option is overpricing. it should be sold.

Arbitrage strategy

Sell one call and Buy stock

At current time, Premium will be received from selling call $26.25

Buy stock @ 74 -74

Total outflow -$47.75

At 6 months, if price of stock is 120

VC for buyer = stock price - E.P.

120 - 100 = 20

Outflow for writer -$20

Selling stock at $120 +120

Interest cost on initial investment

(47.75 * 1%) -0.4775

Total inflows 99.5225

Total gain = total inflows - total outflows

= 99.5225 - 47.75 = 51.7725

Present value of gain = 51.7725/1.01 = $51.26

So, Arbitrage profit of $51.26 will be earned.

jeff jeffy answered 1 year ago

The current stock price is $100, the exercise price is $105.1271, the risk-free interest rate is...

The current stock price is $100, the exercise price is $105.1271, the risk-free interest rate is 5 percent (continuously compounded), the volatility is 30 percent, and the time to expiration is one year (365 days). a. Using the BSM model, compute the call and put prices for a stock option. b. In the previous question (3a) you should get the same price for the call and the put, or very similar (the differences are due to the rounding of the...

What is the price of a European put for Stock at 50, strike at 50, Risk-Free...

What is the price of a European put for Stock at 50, strike at 50, Risk-Free 10%, Volatility at .85 Time at .4167 Pick the closest value? A. 12.34 B. 24.39 C. 10.10 D. 8.94

he current price of a non-dividend paying stock is 40 and the continuously compounded risk-free interest...

he current price of a non-dividend paying stock is 40 and the continuously compounded risk-free interest rate is 4%. The following table gives call and put option premiums for three-month European-style options of various exercise prices. Exercise price Call Premium Put premium 35 5.75 0.40 40 2.29 1.90 45 0.50 5.05 A trader interested in speculating on volatility is considering two investment strategies. The first is a long 40-strike straddle. The second is a long strangle consisting of a long...

The current price of a non-dividend-paying stock is $50. The risk-free interest rate is 1%. Over...

The current price of a non-dividend-paying stock is $50. The risk-free interest rate is 1%. Over the next year, it is expected to rise to $52 or fall to $47. An investor buys a European put option with a strike price of $53. What is the value of the option? Group of answer choices: A: $0.93 B: $1.93 C: $1.95 D: $2.47

The current price of a stock is $ 55.52 and the annual effective risk-free rate is...

The current price of a stock is $ 55.52 and the annual effective risk-free rate is 3.4 percent. A call option with an exercise price of $55 and one year until expiration has a current value of $ 12.80 . What is the value of a put option written on the stock with the same exercise price and expiration date as the call option? Show your answer to the nearest .01. Do not use $ or , in your answer....

The current price of a stock is $32, and the annual risk-free rate is 5%. A...

The current price of a stock is $32, and the annual risk-free rate is 5%. A call option with a strike price of $29 and with 1 year until expiration has a current value of $6.40. What is the value of a put option written on the stock with the same exercise price and expiration date as the call option? Do not round intermediate calculations. Round your answer to the nearest cent.

The current stock price of KMW is $27, the risk-free rate of return is 4%, and...

The current stock price of KMW is $27, the risk-free rate of return is 4%, and the standard deviation is 30%. What is the price of a 63-day call option with an exercise price of $25?

suppose that the stock price $32, the risk-free interest rate is 10% per year the price...

suppose that the stock price $32, the risk-free interest rate is 10% per year the price of a 4 month european call option is $2.85, and the price of a 4 month european put option is $2.65. both options have the strike price $35. describe an arbitrage strategy and justify it with appropriate calculations.

risk free interest rate = 0.08 price of stock at expiration = St St is unknown...

risk free interest rate = 0.08 price of stock at expiration = St St is unknown quantity, st > 0 one contract = 100 share 1. we implement bull put at strike price 47.5 and 42.5 on a stock, receving a net payment or 1.45 on this transaction a. is this buy or selling, call or puts, and which strike price in each case? b. what is the max value profit for one contract? ( T=1/4 (3 months) ) explain...

a) (10 pts) Suppose that the stock price is $31, the risk-free interest rate is 9%...

a) (10 pts) Suppose that the stock price is $31, the risk-free interest rate is 9% per year, the price of a three-month European call option is $2.69, and the price of a 3-month European put option is $2.25. Both options have the strike price $29. Assume monthly compounding. Describe an arbitrage strategy and justify it with appropriate calculations. Please write your solution in complete sentences. b) (10 pts) Use the same data as in part (a), but suppose now...