A financial institution has the following portfolio of options a stock: Type Position Delta of Option...

A financial institution has the following portfolio of options a stock:

Type	Position	Delta of Option	Gamma of Option	Vega of Option
Call	−2,000	0.60	2.5	0.8
Call	−200	0.80	0.6	0.2
Put	−2,000	−0.70	1.1	0.9
Call	−500	0.70	1.8	1.4

In EXCEL file answer the questions below,

An option is available with a delta of 0.5, a gamma of 2, and a vega of 1.5.

(a) What position in the traded option and in the stock would make the portfolio both gamma neutral and delta neutral?

(b) What position in the traded option and in the stock would make the portfolio both vega neutral and delta neutral?

(c) Another option with a delta of 0.2, a gamma of 0.5, and a vega of 1 is available. How could the portfolio become delta, gamma, and vega neutral?

Expert Solution

jeff jeffy answered 2 years ago

A financial institution has the following portfolio of over-the-counter options on sterling: Type Position Delta of...

A financial institution has the following portfolio of over-the-counter options on sterling: Type Position Delta of Option Gamma of Option Vega of Option Call -2,000 0.5 2.2 1.8 Call -1000 0.8 0.6 0.2 Put -4,000 -0.40 1.3 0.7 Call -1000 0.70 1.8 1.4 A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8. Is it possible to find a position in the traded option and in sterling that make the portfolio...

A financial institution has the following portfolio of over-the-counter options on sterling: Type, Position, Delta of...

A financial institution has the following portfolio of over-the-counter options on sterling: Type, Position, Delta of Option, Gamma of Option, Vega of Option ,Call -2,000 ,0.5, 2.2, 1.8; Call -1000, 0.8, 0.6 ,0.2 ;Put -4,000 ,-0.40, 1.3, 0.7 ;Call -1000 ,0.70, 1.8, 1.4; A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8. a. Is it possible to find a position in the traded option and in sterling that make the...

A delta-neutral portfolio has a gamma of -1,500. The delta and gamma of a call option...

A delta-neutral portfolio has a gamma of -1,500. The delta and gamma of a call option are 0.4 and 1.5 respectively. a) How many call options is needed to make it gamma-neutral? b) Making the portfolio gamma-neutral causes the portfolio to no longer be delta-neutral. How many shares of the underlying must be sold to keep it delta-neutral?

A financial institution has the following options for investing funds to a basket of asset consisting...

A financial institution has the following options for investing funds to a basket of asset consisting of fixed income security, bond and highly risky asset. The distributions given below are the two investment options in terms of their return and its associated probability. We define that the profit= 0.9*return – expense. We also assume that the expense for Option A is $1 million and the expense for Option B is $1.8 million. Option A Option B Return ($ millions) Probability...

A financial institution owns a portfolio of options dependent on the US dollar–sterling exchange rate. The...

A financial institution owns a portfolio of options dependent on the US dollar–sterling exchange rate. The delta of the portfolio with respect to percentage changes in the exchange rate is 6.1. If the daily volatility of the exchange rate is 0.5% and a linear model is assumed. The estimated 10-day 99% VaR is $ .

What is the option delta? Delta = Spread of Option Price / Spread of Stock price...

What is the option delta? Delta = Spread of Option Price / Spread of Stock price Spread of Option Price = (40 * 1.2) – 40 = 8 Spread of Stock price = (40 * 1.2) – (40 * 0.833) = 14.7 Delta = 8 / 14.7 Delta = 0.544 What is (1,2) and (0.833) it this calculation?

A long position in a put option can be delta hedged by shorting delta units of...

A long position in a put option can be delta hedged by shorting delta units of the underlying. True or False.

A bank’s position in options on the dollar-euro exchange rate has a delta of 30,000 and...

A bank’s position in options on the dollar-euro exchange rate has a delta of 30,000 and a gamma of -80,000. a) Explain how these numbers can be interpreted. The exchange rate is 0.9 Eur / USD. b) What position would you take to make the position delta neutral? c) After a short period of time, the exchange rate moves to 0.93 Eur / USD. Estimate the new delta. d) What additional trade is necessary to keep the position delta neutral?...

1. Consider the following options portfolio: You write a November 2017 expiration call option on stock...

1. Consider the following options portfolio: You write a November 2017 expiration call option on stock Y with exercise price of $80. You also write a November 2017 put option on stock Y with exercise price of $75. Use the chart below to answer the following: Graph the payoff of this portfolio at expiration as a function of the stock price at that time What will be the profit/loss on this position if stock Y is selling at $77 on...

Roy constructs an options portfolio based on the MXC stock. He writes a call option with...

Roy constructs an options portfolio based on the MXC stock. He writes a call option with exercise price $74 and writes a put option with exercise price $70. Both options have the same expiration date. MXC Call Option price $0.42 Exercise price $74 MXC Put $0.58 $70 Draw the payoff diagram of this portfolio at option expiration as a function of MXC stock price at that time. What will be the profit/loss on this position if MXC is...

Question