Question

A financial institution has just bought 6-month European call options on the Chinese yuan. Suppose that the spot exchange rate is 14 cents per yuan, the exercise price is 15 cents per yuan, the risk-free interest rate in the United States is 2% per annum, the risk-free interest rate in China is 4% per annum, and the volatility of the yen is 12% per annum. Calculate vega of the financial institution’s position. Check the accuracy of your vega estimate by valuing the option at a volatility of 12% and 12.1% sequentially.

Answer #1

Detailed solution is provided.

A financial institution has just bought 6-month European call
options on the Chinese yuan.
Suppose that the spot exchange rate is 14 cents per yuan, the
exercise price is 15 cents per yuan,
the risk-free interest rate in the United States is 2% per annum,
the risk-free interest rate in China
is 4% per annum, and the volatility of the yen is 12% per annum.
Calculate vega of the financial
institution’s position. Check the accuracy of your vega estimate by...

A financial institution has just bought 6-month European call
options on the Chinese yuan. Suppose that the spot exchange rate is
14 cents per yuan, the exercise price is 15 cents per yuan, the
risk-free interest rate in the United States is 2% per annum, the
risk-free interest rate in China is 4% per annum, and the
volatility of the yen is 12% per annum. Calculate vega of the
financial institution’s position. Check the accuracy of your vega
estimate by...

As a financial analyst at JPMorgan Chase investments, you are
evaluating European call options and put options using Black
Scholes model. Suppose BMI’s stock price is currently $75. The
stock’s standard deviation is 7.0% per month. The option with
exercise price of $75 matures in three months. The risk-free
interest rate is 0.8% per month. Please answer the following
questions.
Please choose all correct answers.
1.
The price of the European call option is
$13.14
2.
The price of the...

As a financial analyst at JPMorgan Chase investments, you are
evaluating European call options and put options using Black
Scholes model. Suppose BMI’s stock price is currently $75. The
stock’s standard deviation is 7.0% per month. The option with
exercise price of $75 matures in three months. The risk-free
interest rate is 0.8% per month. Please answer the following
questions.
which one is the correct answers
1.
The price of the European call option is $13.14
2.
The price of...

What is the delta of a short position in 1,000 European call
options on Silver futures? The options mature in 8 months and the
futures contract underlying the option matures in 9 months. The
current 9-month futures price is €8 per ounce, the exercise price
of the options is €8, the risk-free rate is 12% per annum, and the
volatility of silver is 18% per annum.

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...

(a) What is a lower bound for the price of a 6-month European
call option on a nondividend-paying stock when the stock price is
$50, the strike price is $48, and the risk-free interest rate is 5%
per annum? (b) What is a lower bound for the price of a 2-month
European put option on a nondividend-paying stock when the stock
price is $70, the strike price is $73, and the risk-free interest
rate is 8% per annum?

A 3-month European call on a futures has a strike price of $100.
The futures price is $100 and the volatility is 20%. The risk-free
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of the call option? (Use Black-Scholes-Merton valuation for futures
options)

What is the price of a European call option on a
non-dividend-paying stock when
the stock price is $52, the strike price is $50, the risk-free
interest rate is 12% per annum, the
volatility is 30% per annum, and the time to maturity is three
months? (Hint: Remember Black-
Sholes-Merton Model. Please refer to the N(d) tables provided to
you to pick the N values you
need)

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...

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