Question

A spot price of an asset has an expected return of 16% and a volatility of 35%. The current price is $38.

- What is the probability that a European call option on the asset with an exercise price of $40 and a maturity date in six months will be exercised?
- What is the probability that a European put option on the asset with the same exercise price and maturity will be exercised?

Answer #1

3. A stock price follows geometric Brownian motion with an
expected return of 16% and a volatility of 35%. The current price
is $38. a) What is the probability that a European call option on
the stock with an exercise price of $40 and a maturity date in six
months will be exercised? b) What is the probability that a
European put option on the stock with the same exercise price and
maturity will be exercised?

2.1 A stock price has an expected return of 15% and a volatility
of 25%. It is currently $56.
2.1.1 What is the probability that it will be greater than $85 in
two years? (4)
2
2.1.2 What is the stock price that has a 5% probability of being
exceeded in two years? (2)
2.2 A binary option pays off $150 if a stock price is greater than
$40 in three months. The
current stock price is $35 and its...

Suppose a stock has an expected return of 10% per year and a
return volatility of 28% per year and equally likely transitions
(i.e. with probability 1/2). The risk-free rate is 4% per year. The
stock has a current price of $100 and has declared dividends of
$2.04 to be paid at the end of each six-month period.
Construct a binomial model for the stock price of ABC with 2
semi-annual periods.
Find the value of a European call option...

The price of a European call that expires in six months and has
a strike price of $28 is $2. The underlying stock price is $28, and
a dividend of $1 is expected in 4 months. The term structure is
flat, with all risk-free interest rates being 6%. If the price of a
European put option with the same maturity and strike price is $3,
what will be the arbitrage profit at the maturity?

GIVEN:
Spot price = $50
Strike Price = $54
Time to expiration = 6 months
Risk Free rate = 3%
Variance = 22% (use for volatility)
FIND:
Price of a European Put option
Price of a European Call option
Show work and formula

Suppose the current spot exchange rate between the U.S.
dollar and British pound is $1.6/£. A European call option on
pounds is expiring today. The call option has an exercise price of
$1.56/£. At the same time, a European put option on pounds is
expiring today. The put option has an exercise price of $1.65/£. 2
points
Given the information above, which of the following is
correct?
both the call option and the put option are out-of-the-money.
both the call...

Consider an option on a non-dividend-paying stock when the
stock is $ 30, the exercise price is $29. The risk –free rate is 5%
per annum, the volatility is 25% per annum, and the time to
maturity is four months.
(a) What is the price of the option if it is European
call?
(b) What is the price of option if it is an American
call?
(c) What is the price of the option if it is a European
put?

A European put option is currently worth $3 and has a strike
price of $17. In four months, the put option will expire. The stock
price is $19 and the continuously compounding annual risk-free rate
of return is .09. What is a European call option with the same
exercise price and expiry worth? Also, given that the price of the
call option is $5, show how is there an opportunity for
arbitrage.

1. Suppose that firm Ds shares are currently selling for $38.
After six months it is estimated that the share price will either
rise to $43.32 or fall to $33.82. If the share price rises to
$43.32 in six months, six months from that date (1 year from today)
the price is estimated to be either $49.38 or $38.55. If the share
price falls to $33.82 in six months, six months from that date (1
year from today) the price...

Asset A has an annual expected return of 12%, and an annual
volatility of 30%. Asset B has an expected return of 4%, and a
volatility of 10%. The covariance of the returns of A and B is
0.02. What is the volatility of the portfolio that is composed of
70% asset A, and 30% asset B? [note: answer have been rounded to
the percent]

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