By this author

Calculation of the convexity adjustment to the forward rate in the Vasicek model for the forward exotic contracts

Issue 3 from 22.09.2022

In the following article, we consider forward contracts, which are financial instruments used to buy or sell some assets at a certain point moment in the future, and at the fixed price. Such contracts are customizable and traded over-the-counter, unlike futures, which are standardized contracts traded at exchanges. Particularly, we focus on in-arrears interest rate forward contracts (in-arrears FRA). The difference from the vanilla FRA: floating rate is immediately paid after it is fixed. We calculate the convexity adjustment to the forward simple interest rate in the single-factor Vasicek stochastic model for such contracts with different payment dates. With the help of the no-arbitrage market condition it is shown that such adjustments should be non-negative when payments occur before the end of accrual period and should be negative when payments occur after accrual period. We also studied in-arrears forward and option contracts, where fixed interest rate and principal, on which this rate is accrued, are denominated in different currencies (so called quanto in-arrears FRA and quanto in-arrears options). We checked that quanto in-arrears FRA equals in-arrears FRA in case when rates and principal are from the same currency market, and that quanto in-arrears option contract prices are greater than those of vanilla options.

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