Question

1- A one-year European call option on Stanley Industries stock with a strike price of $55 is currently trading for $75 per share. The stock pays no dividends. A one-year European put option on the stock with a strike price of $55 is currently trading for $100. If the risk-free interest rate is 10 percent per year, then what is the current price on one share of Stanley stock assuming no arbitrage?

2- The current price of MB Industries stock is $20 per share. In the next year the stock price will either go up to $24 per share or go down to $16 per share. MB pays no dividends. The one year risk-free rate is 5 percent and will remain constant. Using the one-step binomial pricing model, what is the price of a one-year CALL option on MB stock with a strike price of $20 (out to two decimal places)?

3- The current price of MB Industries stock is $20 per share. In the next year the stock price will either go up to $24 per share or go down to $16 per share. MB pays no dividends. The one year risk-free rate is 5 percent and will remain constant. Using the one-step binomial pricing model, what is the price of a one-year CALL option on MB stock with a strike price of $20 (out to two decimal places)?

4- A European call and a European put on the same stock have the exact same strike price and the exact same expiration. At 10:00am on a certain day, the call option premium is $3.25 and the put option premium is $4.25. At 10:01am news reaches the market that no effect on the stock price or on interest rates, but it does increase volatilities. As a result, the call premium increases to $4.00. What is the new put premium (out to two decimal places)?

Answer #1

From the put call parity equation

c+ K/(1+r)^t = p+S

where c and p are call and put option premiums respectively

K is the strike price of the options

, r is the periodic interest rate

and t is the no. of periods

, S is the spot price of stock

For no arbitrage, the put-call parity must hold

S = 75+55/1.1-100 =$25

**No arbitrage price of Stanley's stock is
$25**

**(It may be noted that European Put option cannot trade
above present value of strike price ie. $50, Also European call
option cannot trade above current stock price i,e,
$25)**

The current price of MB Industries stock is $20 per share. In
the next year the stock price will either go up to $24 per share or
go down to $16 per share. MB pays no dividends. The one year
risk-free rate is 5 percent and will remain constant. Using the
one-step binomial pricing model, what is the price of a one-year
CALL option on MB stock with a strike price of $20 (out to two
decimal places)?

The current price of MB Industries stock is $20 per share. In
the next year the stock price will either go up to $24 per share or
go down to $16 per share. MB pays no dividends. The one year
risk-free rate is 5 percent and will remain constant. Using the
one-step binomial pricing model, what is the price of a one-year
PUT option on MB stock with a strike price of $20
(out to two decimal places)?

1. Luther Industries is currently trading for $28 per share. The
stock pays no dividends. A one-year European put option on Luther
with a strike price of $30 is currently trading for $2.55. If the
risk-free interest rate is 6% per year, compute the price of a
one-year European call option on Luther with a strike price of
$30.
The price of one-year European call option on Luther
with a strike price $30 is ______$ (round to four
decimal places)....

A European call option on a stock with a strike price of $50 and
expiring in six months is trading at $14. A European put option on
the stock with the same strike price and expiration as the call
option is trading at $2. The current stock price is $60 and a $1
dividend is expected in three months. Zero coupon risk-free bonds
with face value of $100 and maturing after 3 months and 6 months
are trading at $99...

A European call option on a stock with a strike price of $50 and
expiring in six months is trading at $14. A European put option on
the stock with the same strike price and expiration as the call
option is trading at $2. The current stock price is $60 and a $1
dividend is expected in three months. Zero coupon risk-free bonds
with face value of $100 and maturing after 3 months and 6 months
are trading at $99...

A European call option on a stock with a strike price of $75 and
expiring in six months is trading at $5. A European put option on
the stock with the same strike price and expiration as the call
option is trading at $15. The current stock price is $64 and a $2
dividend is expected in three months. Zero coupon riskāfree bonds
with face value of $100 and maturing after 3 months and 6 months
are trading at $99...

There is a six month European call option available on XYZ stock
with a strike price of $90. Build a two step binomial tree to value
this option. The risk free rate is 2% (per period) and the current
stock price is $100. The stock can go up by 20% each period or down
by 20% each period.
Select one:
a. $14.53
b. $17.21
c. $18.56
d. $12.79
e. $19.20

38. Calvin Industries is currently trading for $27 per share.
The stock pays no dividends. A one-year European put option on
Calvin with a strike price of $30 is currently trading for $2.60
and a one-year European call option on Calvin with the same strike
price and remaining time to maturity as the European put is trading
for $1.30. The annual risk-free rate comes closest to: A) 5.7%. B)
5.8% C) 5.9% D) 6% Ans: D

The price of a European call option on a non-dividend-paying
stock with a strike price of $50 is $6. The stock price is $51, the
continuously compounded risk-free rate (all maturities) is 6% and
the time to maturity is one year. What is the price of a one-year
European put option on the stock with a strike price of $50?
a)$9.91
b)$7.00
c)$6.00
d)$2.09

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...

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