b. A financial institution has the following portfolio of over-the-counter options. Option Position Delta of Option W 120 0.9 X -80 1.2 Y 250 + (20 x Y) -0.8 Z -180 0.9 Gamma of Option 1.8 0.5 1.1 1.7 Vega of Option 1.5 0.4 0.9 1.2 Traded option A is available with a delta of 0.3, a gamma of 1.2, and a vega of 0.5. Traded option B is available with a delta of 0.6, a gamma of 1.8, and a vega of 0.9. What position in the traded options and in underlying stock would make the portfolio delta neutral, gamma neutral and vega neutral? (9 marks)

Consider two put options on different stocks. The table below reports the relevant information for both options: Put optionTime to maturityCurrent price of underlying stockStrike priceVolatility ( )X1 year$27$1830%Y1 year$25$2030%All else equal, which put option has a lower premium? A.Put option Y B.Put option X

Label the following for this diagram: a. Name of options payoff b. Identify whether positive or negative premium c. Identify breakeven point d. What is the profit or loss when stock price is S60 at maturity e. Suppose you have this options position, should you exercise your right (if any) assuming that the stock price is $60 at maturity? Option Payoffs and Profits Long put $40 $20 $0 Option Payoff Option Profit Exerche Price $20 S40 $20 $40 S60 $80. Stock Price At Maturity Payoff and Profit

An option is trading at $3.45. If it has a delta of .78, what would the price of the option be if the underlying increases by $.75? A. What would the price of the option be if the underlying decreases by $.55? B. What makes this a call option? C. With a delta of .78, is this option ITM, ATM or OTM and how?

You are pricing options with the following characteristics: •Current stock price (St): $35.60 •Exercise price (X): $50 •Time to expiration (T-t): 9 months •Risk-free rate (rf): 3.25% •Volatility (0): 45% (a): What is the Black-Scholes value of call option? In your hand-written solution, provide the calculations of d1,d2, and the final call price. Use Excel or another spreadsheet program to compute the values of N(d1) and N(d2). See the notes for details. (b): Using put-call parity, what is the value of a put option? For this case, assume continuous compounding, which implies that PVt(X)=e-r(T-t).X.

Q2: Given the following inputs for YMMV: Interest rate 3.25 Dividend rate 3.00 Spot Price Volatility (%) 30.21 12.00 Strike Price 30.00 Expiry (months) T Option type 12 European Put a) Compute u, d, Pup; Pdn, Construct a 3 step tree and price the option.

Consider a portfolio that consists of the following four derivatives: 1) a put option written(sold) with strike price K − 5, 2) a call option purchased with strike price K − 5, 3) a call option written(sold) with strike price K + 5, and 4) a put option purchased at strike price K + 5. All options are European.The risk-free rate is rf , the time to expiration is T, the initial stock price is S0, and the stock price atmaturity is ST . What are the payoffs at expiration of this portfolio? What must the price of this portfoliobe?

Answer the following two questions with respect to the table below. A financial institution has the following portfolio of over-the-counter options on a stock: Vega of Option Туре Рosition Delta of Gamma of Option Option 0.50 Call -1,000 -500 2.2 1.8 Call 0.80 0.6 0.2 Put -2,000 -500 -0.40 1.3 0.7 Call 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. What position in this option and the underlying will make the portfolio delta and gamma neutral?

A financial institution has the following portfolio of over-the-counter options on GBP (sterling, UK currency): Type Position Delta of Option Gamma of Option Vega of Option Call -1,000 0.5 2.2 1.8 Call -500 0.8 0.6 0.2 Put -2,000 Call -500 -0.40 0.70 1.3 0.7 1.8 1.4 A traded option is available with a delta of 0.3, a gamma of 1.7, and a vega of 0.8. To make the portfolio both gamma-neutral and delta-neutral, you will take a (long/short) position in the traded option. You will also take a (long/short) position in GBP. How many GBP (i.e. don't worry about L/S, just write how many GBP)? Assume that all implied volatilities change by the same amount so that vegas can be aggregated. Enter your answer rounded to the nearest integer, skip the currency sign. For example, if your calculation results in GBP 9,876.1234567, you only need to enter 9876

I2 Consider a pair of call and put options with the same expiration date but different strike prices. Theput option has a strike price of $45 and is currently priced at $6.00. The call option has a strike priceof $35 and is currently trading at a price of $6.50. The current stock price is $40 per share. A traderis evaluating a trading strategy involving the following option positions: Long 1 put options (with strike price $45) Long 2 call option (with strike price $35)   a)Draw a figure/graph illustrating the profit/loss of the trading strategy. Make sure you scale and labelall the lines and points properly so that gains and losses are clearly shown.b)For what range of stock prices would the trader end up with a profit if the strategy is executed?c)Discuss the main characteristics of this strategy. When is it appropriate to use such a strategy?