In a lot of ways.
Cross-currency swaps on GBPUSD and/or EURGBP. Or synthetically replicate the Greeks by taking positions in USD denominated assets. Most favorable outcome will be achieved if you find a cointegrated series that match, as well as the pure joint distribution (the copula, stripping away the marginals) so you don't have to rebalance all the time.
Thank you for your reply. Regarding the FX Swaps it was my first thought, but the time I tried to set up an example in my mind I found out that I didnt know what amount/Principal to hold for the FX Swaps....Suppose a dummy position on EURGBP with face 100 mil EUR and strike 0,9. How I should calculate the principal of the swaps? Could you please explain further the methodology? Additionally, could you also explain further the second solution?
I apologize if my questions are dummy, but I'm not a quant expert
Once again thanks a lot for your assistance and time you spent to reply
The bank has a position on USDRUS options that has a delta of $2m and a gamma of $0.4m (per 1% move). The USDRUS exchange rate is 14.2. What position would you take to make the position delta neutral? After a short period of time, the USDRUS exchange rate moves to 13.916. Estimate the new delta. What additional trade is necessary to make the position delta neutral?
How does one hedge delta in the FX market?
I can only think of selling a call option, which will get rid of the gamma. This short call will possible reduce some of the delta, but how do you think about hedging the rest of the delta? Futures/forwards?
Hi @WhizzKidd It's sometimes easier to help if we know the source (i.e., what is the source?) because some sources are more reliable than others. It appears we are given position delta without knowing the percentage greeks or actual position sizes (see https://www.bionicturtle.com/forum/threads/l1-t4-7-dynamic-delta-hedging.4839/ for introduction to distinction between position greeks and percentage greeks). If the goal is to neutralize both gamma and delta, we could (i) enter a short position in call options (i.e., with negative position gamma) and then (ii) short shares to neutralize the remaining positive position delta. So, typically you'd neutralize the gamma first and then the delta because shorting shares will neutralize the delta without impacting gamma; but options have both delta and gamma.
But the questions asks only "What position would you take to make the position delta neutral?" which can be achieved with a short currency futures contract, in this case with an approximate (the future has percentage delta of almost one) notional of $2.0 mm. We neutralize position delta on a dollar-for-dollar basis. The gamma will remain. Then, with respect to "After a short period of time, the USDRUS exchange rate moves to 13.916. Estimate the new delta.", I suppose the question is looking for: that's a 13.916/14.20-1 = -2.00% move exactly, such that the new delta = $0.40 * -2.0% = -$0.80 on the net position; or maybe it looking for the $2.0 mm - 2%*0.40 = $1.2 mm on the original exposure. I hope that helps!
@WhizzKidd yes, right, thanks! I guess since gamma is given as $0.4 m/.010 (ie, $0.4 per 1%), it is $0.4 m/Δ0.01 * Δ0.02 = $0.40 * 0.02/0.01 = $0.40 * 2, just as you say . Gamma is tricky because while delta is elegantly unit-less (delta = $Δc/$ΔS so dollars cancel), gamma's true units are un-intuitively denominated (1/$) since gamma is Δdelta/ΔS =Δ($Δc/$ΔS)/$ΔS = unit-wise Δ($/$^2) = Δ(1/$). Thanks!