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

A financial institution has the following portfolio of over-the-counter options on sterling: Type Call Call Put Call Position -1,000 -500 -2,000 -500 Delta of Option 0.5 0.8 -0.40 0.70 Gamma of Option 2.2 0.6 1.3 1.8 Vega of Option 1.8 0.2 0.7 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) What position in the traded option and in sterling would make the portfolio both gamma neutral and delta neutral? (b) What position in the traded option and in sterling would make the portfolio both vega neutral and delta neutral?

2. These options are traded in the market: call option with an Exercise (Strike) Price of 1.15 $/€ and premium (option cost) of 0.03 $ per euro. (a) If the Spot exchange rate is 1.17 $/ €, is the option ITM, ATM or OTM? (b) Calculate Intrinsec value and Time value of the option. (c) If put options are traded with same Exercise Price at same cost of 0.03 $ per euro and Fwd for the same maturity is traded at 1.17 $/ €, how can an astute tradem arbitrage? Explain. (d) Calculate Intrinsec value and Time value of the put option mentioned above.

A financial institution has thefollowing portfolio of ove over-the- counter derivatives on pounds sterling: Туре Position Delta of Gamma of Vega of -1,000 2,000 -500 1,000 Option Forward Option Forward Option/Forward 2.2 1.3 1.8 Call 0.5 1.8 Put Call -0.4 0.7 0.7 1.4 Forward -1 A traded option is available with a delta of 0.6, a gamma of 1.5, and a vega of 0.8. (a) What position is the traded option and in pounds sterling would make the portfolio both gamma neutral and delta neutral? Solution: The delta of the portfolio is -1,000 x 0.5 - 2000 x (-0.4) - 500 x (0.7) + 1,000 x (-1) = -1050 The gamma of the portfolio is-1,000 x 2.2 –2,000 x 1.3 - 500 x 1.8+ 1000 x 0 = - 5,700 The vega of the portfolio is -1,000 x 1.8 – 2,000 x 0.7 - 500 x 1.4 +1,000 x 0= -3,900 A long position in 3,900 traded options will give a gamma-neutral portfolio since the long position has a gamma of 3,900 x 1.5 = +5,850. The delta of the whole portfolio (including traded options) is then: 3,900 x 0.6 - 1050 =…