Determine your current portfolio delta gamma and vega

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The following table lists three financial instru- ments and their deltas, gammas, and vegas for each $1 million notional principal under the assumption of a long position. (Long in a swap  or FRA means to pay fixed and receive floating.)

Assume that  you hold  a $12 million  notional principal long position in the three-year call option, an $8 million notional principal short position in the three-year swap, and an $11 million notional principal long position in the FRA. Each derivative is based on the 90-day LIBOR.

Instrument

Delta

Gamma

Vega

3-year call option with

$40

$1,343

$5.02

exercise rate of 0.12

 

 

 

3-year swap with fixed

$152

-$678

$0

rate of 0.1125

 

 

 

2-year FRA with fixed

$72

-$390

$0

rate of 0.11

 

 

 

a. As described above, you have three instru- ments currently in your  portfolio.  Determine your current portfolio  delta,  gamma, and vega. Describe in words the risk prop- erties of your portfolio based on your calculations.

b. Assume that you have to maintain  your current position in the call option but are free to increase or decrease your positions  in the swap and FRA and you can add a position in a one-year call with a delta of $62, a gamma of $2,680,  and a  vega of $2.41. Find the combination of notional principals  that  would  make  your overall position be delta hedged, gamma hedged, and  vega hedged.

Reference no: EM13925647

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