Related questions

• What does it mean to assert that the theta of an option position Hint: A theta of -0.1 means that if delta t units of time pass with no change in either the stock price or..
• The Black–Scholes price of an out-of-the-money call option with an exercise price Hint: The strategy costs the trader 0.10 each time the stock is bought or sold. The total expected cost of..
• Suppose that a stock price is currently $20 and that a call option with an exercise price Hint: The holding of the stock at any given time must be N(d1) . Hence the stock is bought just after the ..
• A company uses delta hedging to hedge a portfolio of long positions in put and call options on a currency Hint: A long position in either a put or a call option has a positive gamma. From Figure 17.8, when gamma ..
• Repeat Problem 17.13 for a financial institution with a portfolio of short positions Hint: A short position in either a put or a call option has a negative gamma. From Figure 17.8, when gamma..
• Under what circumstances is it possible to make a European option on a stock index both gamma neutral and vega neutral Hint: ..
• Repeat Problem 17.17 on the assumption that the portfolio has a beta Hint: When the value of the portfolio goes down 5% in six months, the total return from the portfolio, inc..
• Show by substituting for the various terms in equation Hint: ..
• Suppose that $70 billion of equity assets are the subject of portfolio insurance schemes Hint: We can regard the position of all portfolio insurers taken together as a single put option. The thre..
• Does a forward contract on a stock index have the same delta as the corresponding futures contract? Hint: With our usual notation the value of a forward contract on the asset is S0e-qT -Ke-rT. When the..
• A bank’s position in options on the dollar–euro exchange rate has a delta Hint: The delta indicates that when the value of the euro exchange rate increases by $0.01, the value of t..
• Consider a one-year European call option on a stock when the stock price is $30 Hint: The price, delta, gamma, vega, theta, and rho of the option are 3.7008, 0.6274, 0.050, 0.1135,-0.005..
• Suppose that a second traded option with a delta of 0.1 Hint: Let w1be the position in the first traded option and w2 be the position in the second traded op..
• A deposit instrument offered by a bank guarantees that investors will receive a return Hint: The product provides a six-month return equal to max (0,0.4R)where R is the return on the index..
• Use DerivaGem to check that equation (17.7) is satisfied for the option considered Hint: For the option considered in Section 17.1, ..
• Use the DerivaGem Application Builder functions to reproduce Table 17.2 Hint: Consider the first week. The portfolio consists of a short position in 100,000 options and a long po..