Currency Swap Forward Rate

[hmehrotra]

Hi David,

I am trying to understand the valuation of currency swap based on FRAs and struggling with how you have calculated Forward rate using IRP. The formula that you have used is =spot_dollar_yen*EXP((US Rate - Japanese rate)*Time). I am familiar with the following formula -
Forward Rate = Spot * (1+ domestic/1+Foreign) ^ T. Please explain.

Thanks,
CF

 

[David Harper CFA FRM]

Hi CandidFRM,

Both are good, only difference is compound frequency assumption (as the assignment is Hull here, I follow him with continuous):
IRP says under continuous Spot*exp(domestic*T) = Forward*exp(foreign*T), which solves for Forward as you have above, under continuous assumption.

Yours starts with:
Spot*(1+domestic)^T = Forward*(1+foreign)^T; i.e., annual compounding
so Forward = Spot*(1+domestic)^T / (1+foreign)^T = Spot*((1+domestic)/(1+foreign))^T

Hope that helps, David

 

[hmehrotra]

David,

Thanks for the quick reply. That was easy. Is there an easy way to remember when to use continuous v/s discreet? Sometimes it is clear but other times I miss it completely.

 

[David Harper CFA FRM]

Hi CandidFRM,

I don't think there is a right/wrong circumstance, that I am aware. From an exam perspective, it absolutely should be specified.
One practical thing that separates them (aside from the popularity of continuous in academics b/c it's so much easier to manipulate LN() and EXP()) is:
log returns add over time ("time additive" as Linda allen says) but not across portfolio components,
discrete returns are just the opposite
a bit of background here: http://www.bionicturtle.com/learn/article/why_we_use_log_returns_in_quantitative_finance_frmquant_xls/

e.g., Grinold (assigned Ch7 & 17) is mostly aggregating cross-sectionally (building up returns) so the discrete are more natural for him

..but no right/wrong ...in response to this question http://forum.bionicturtle.com/viewreply/3772/
i added the third page in the swap valuation just to show that it can be done entirely in semi-annual.

David