Статьи автора

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

Номер 3 от 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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Multidimensional coherent risk measures and their properties

Номер выпуска 3 от 18.12.2025

Coherent risk measures are widely used in practice to calculate risk. Multidimensional coherent risk measures are important to use for companies and banks operating in different international markets. Here we introduce an example which clearly shows that multidimensional coherent risk measures reduce capital requirements on multi-asset or multi-currency markets. In this paper we consider two different approaches to define multidimensional coherent risk measures. The first approach is based on a cone-based exchange rate set, whereas the second employs random sets to account for liquidity constraints and other market frictions. Also constructive approach for multidimensional risk measures using one-dimensional law invariant ones is considered. We introduce the example of coherent risk measure which cannot be represented by the constructive approach. Two important properties of multidimensional risk measures such as law invariance and space consistency are investigated and their equivalent properties in terms of determining set and acceptance set are given. Then we consider a multidimensional generalization of Tail VaR and show that it satisfies space consistency and law invariance properties and provide an example which shows that multidimensional portfolio risk estimation using this risk measure gives an adequate result.

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