$ rho = KTe^{-r_f T}\Phi(d_2) $

$ rho_f = STe^{-r_f T}\Phi(d_1)$

$ rho = c(r=6.8438\%)-c(r=5.8438\%)$

$ rho_f =c(r_f=7.915\%)-c(r_f=6.915\%) $

$ \text{Rho} = KTe^{-r_f T}\Phi(d_2) $

$ \text{Rho}_f = STe^{-r_f T}\Phi(d_1)$

$ \text{Rho} = c(r=6.8438\%)-c(r=5.8438\%)$

$ \text{Rho}_f =c(r_f=7.915\%)-c(r_f=6.915\%) $

I would like to replicate the whole "Taleb \$-value column" in the below Table. Take the Delta, which is around 0.50. How do you calculate its value in dollars?

Please, let me know if more details are needed. Thanks for the help.

I would like to replicate the whole "Taleb \$-value column" in the below Table. Take the Delta, which is around 0.50. How do you calculate its value in dollars? Since it is negative, is the trader selling GBP or USD?

Please, let me know if more details are needed. Thanks for the help. I am new to FX Options.

Again, thanks for the help.

I'm trying to replicate the Example given in pag. 229-230 of Dynamic Hedging by N. Taleb and I am not sure on how to convert the Greeks in Dollars, how the author is computing the Greeks and how he is computing the call price.

Start with a currency position in GBP-USD. Spot is 1.605. The trader buys a 6-month call (183 days) in the amount of GBP 100 mil. The price is 4.578% and the trader pays $4'578'000. USD rate is 5.8438% (yearly) and GBP is 6.915%.

He computes the Forward exchange rate to be 1.5973. I suppose that this is the strike price used in the computation.

Call price: He states at the beginning of the book that the market always trades at 100. So I computed the call price in this way by using the Black-Scholes formula reported in th Appendix: $$ c = \text{BS}(S=\frac{1.6050}{1.6050},K=\frac{1.5973}{1.6050},t=\frac{183}{360},\sigma=15.7\%,r=5.8438\%,r_f=6.915\%)=0.0427986 $$

Questions:

I'm trying to replicate the Example given in pag. 229-230 of Dynamic Hedging by N. Taleb and I am not sure on how to convert the Greeks in Dollars and how the author is computing the Greeks.

Start with a currency position in GBP-USD. Spot is 1.605. The trader buys a 6-month call (183 days) in the amount of GBP 100 mil. The price is 4.578% and the trader pays $4'578'000. USD rate is 5.8438% (yearly) and GBP is 6.915%. He computes the Forward exchange rate to be 1.5973.

I managed to obtain the call value with BS (see formula in the Appendix) by supposing the market trades at 1, thus dividing the spot rate and the strike (=1.5973 I suppose) by the spot rate.

I would like to replicate the whole "Taleb \$-value column" in the below Table. Take the Delta, which is around 0.50. How do you calculate its value in dollars?

Bonus Part for the ones willing to read everything

Bonus Questions: