Exotic Derivatives Trading

February 19, 2009

Himalayas – “Correga Reversal and hedging it”

Filed under: Risk Management of Exotic Derivatives — Exotics Trader @ 3:38 pm

Consider a two asset Himalaya under the following circumstances.
1. The option is nearing its first Observation date

2. Both the assets have similar spot levels
3. Let’s say asset A ~ 96% and asset B at ~ 100%
4. Also vols of both the assets are significantly different.
Vol A = 40%, Vol B = 20%
Clearly the long position holder wants B to knock out since option on A is costly than option on B.
Keep in mind, What makes structure costly: Higher probability of B knocking out.

When A ~ 96% and B ~ 100%
At +1 correl there are two possible movements,
a) Both the spots increase: (B moves by x, A moves by 2x), therefore B
has to move by at least 4% for A to outperform B.
b) Both the spots decrease (leftward movement on the spot line)
A is always the worst performer.

At -1 correl, again there are two possible movements ,
a) Both move towards each other: (B moves by -x, A moves by +2x),
therefore B has to move by at least -1.33% for A to outperform B
b) Both move away from each other: A is always the worst performer.

Clearly the probability of A outperforming B is more at -1 correl and as a long position holder I don’t want A to knock out, hence structure is long correlation.

Reverse the spots of A and B and carry out a similar exercise to discover that structure is short correlation.

Hence when spot of A is less than spot of B, structure is long correlation/cross gamma and when A crosses B structure is short correlation/crossgamma.

Hedging
:
1. Buy an Outperformance digital(Call spread) on (A-B) so when A>B structure is long correlation and when spot of A is less than spot of B (outperformance is OTM) structure is short correlation. Add this cost of hedging when pricing Himalayas.
OR
2. Find the probability of A knocking out on the basis of vols and correlation. Sell call on A in proportion to that probability factor and do a similar exercise for B as well.
OR
3. Monitor the implied and realized covariance’s and re balance the delta accordingly

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