Question
In: Accounting
Peter has just sold a European call option on 10,000 shares of a stock. The exercise...
Peter has just sold a European call option on 10,000 shares of a stock. The exercise price is $50; the stock price is $50; the continuously compounded interest rate is 5% per annum; the volatility is 20% per annum; and the time to maturity is 3 months.
(a) Use the Black-Scholes-Merton model to compute the price of the European call option.
(b) Find the value of a European put option with the same exercise price and expiration as the call option above.
(c) What position should Peter take in the stock for delta neutrality?
(d) Suppose that Peter does set up a delta neutral position as soon as the option has been sold and the stock price jumps to $55 within the first hour of trading. What trade is necessary to maintain delta neutrality?
Solutions
ekkarill92 answered 2 years agoRelated Solutions
Peter has just sold a European call option on 10,000 shares of a stock. The exercise...
Peter has just sold a European call option on 10,000 shares of a
stock. The exercise price is $50; the stock price is $50; the
continuously compounded interest rate is 5% per annum; the
volatility is 20% per annum; and the time to maturity is 3
months.
(a) Use the Black-Scholes-Merton model to compute the price of
the European call option.
(b) Find the value of a European put option with the same
exercise price and expiration as the call...
Peter has just sold a European call option on 10,000 shares of a stock. The exercise...
Peter has just sold a European call option on 10,000 shares of a
stock. The exercise price is $50; the stock price is $50; the
continuously compounded interest rate is 5% per annum; the
volatility is 20% per annum; and the time to maturity is 3
months.
(a) Use the Black-Scholes-Merton model to compute the price of
the European call option.
(b) Find the value of a European put option with the same
exercise price and expiration as the call...
A fund manager has just sold a call option on 100 shares of a stock. The...
A fund manager has just sold a call option on 100 shares of a
stock. The stock price is $87 and its volatility is 20% per annum.
The strike price of the option is $89 and it matures in 6 months.
The risk-free rate is 6% per annum (continuously compounded).
a) What position should the fund manager take in the stock to
achieve delta neutrality?
b) Suppose after the fund manager sets up the delta neutral
position, the stock price...
A bank has sold for $300,000 a European call option on 100,000 shares of a non-dividend...
A bank has sold for $300,000 a European call option on 100,000
shares of a non-dividend paying stockS0 = 49, K = 50, r = 5%, s =
20%, T = 20 weeks, m = 13%The Black-Scholes-Merton value of the
option is $240,000 , how do you get to $240,000 ?
Suppose that a financial institution has sold for $300,000 a European call option on 100,000 shares...
Suppose that a financial institution has sold for $300,000 a
European call option on 100,000 shares of a non-dividend stock.
Assume that the stock price is $49, the strike price is $50, the
risk-free interest rate is 5% per annum, the stock price volatility
is 20% per annum, the time to maturity is 20 weeks (0.3826 years),
and the expected return from the stock is 13% per annum.
(b) (Strategy 1) The financial institution decides to do nothing
but deposit...
please fast A bank has just sold 500,000 call options on shares of a stock. The...
please fast
A bank has just sold 500,000 call options on shares of a stock.
The strike price is 40; the stock price is 40; the continuously
risk-free rate is 5%; the volatility is 30%; and the time to
maturity is 0.25. What position should the company take in the
stock for delta neutrality?
A European call option on Visa stock costs $85.36, while a European put option on the...
A European call option on Visa stock costs $85.36, while a
European put option on the same stock costs $31. Both options
expire in 0.5 years and have a strike price of 800. Google does not
pay dividends and its stock price is $850.
What should be the risk-ree rate (effective annual rate)?
. A stock sells for $110. A call option on the stock has an exercise price...
. A stock sells for $110. A call option on the stock has an
exercise price of $105 and expires in 43 days. If the interest rate
is 0.11 and the standard deviation of the stock’s return is 0.25.
a) Calculate the call using the Black-Scholes model b) What would
be the price of a put with an exercise price of $140 and the same
time until expiration? c) How does an increase in the volatility
and interest rate changes...
what is the value of a european call option with an exercise price of $40 and...
what is the value of a european call option with an
exercise price of $40 and a maturity date six months from now if
the stock price is $28 the instantaneous variance of the stock
price is 0.5 and the risk free rate is 6% use both a) two step
binomial tree b) black scholes pricing formula
Consider a European call option and a put option on a stock each with a strike...
Consider a European call option and a put option on a stock each
with a strike price of K = $22 and each expires in six months. The
price of call is C = $3 and the price of put is P = $4. The risk
free interest rate is 10% per annum and current stock price is S0 =
$20. Show how to create an arbitrage strategy and calculate the
arbitrage traders profit.
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