Browsing by Author "Mc Walter Thomas"

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    Application of Effective Markovian Projection to SABR and Heston Models
    (2023) Bagraim, Jacques; Ouwehand, Peter; Mc Walter Thomas
    Model flexibility is often at odds with tractable pricing, and models with tractable pricing often lack flexibility. This poses an issue when calibrating a model to market data where tractability and flexibility are both required. We investigate an approach that allows one model to be projected onto another, potentially allowing for a flexible model to be represented by a tractable one. Here, Effective Markovian Projection is used to obtain equivalent Heston model parameters from a range of SABR models with different skew parameters using two distinct point-matching algorithms. The implied parameters are used to price European claims under a variety of schemes in order to outline the efficacy in this context. We see that this technique is accurate when the underlying probability densities of both models match closely, i.e., when the SABR skew parameter approaches unity, as is seen by comparing prices of claims using Classic Markovian Projection where the underlying SABR processes share the same density. PDE and perturbation SABR prices match closely while Heston characteristic function prices become unstable at lower skew parameters and far in-the-money and out-the-money values of the strike. Lastly, a potential improvement to this application involving error-correction terms is proposed for further application.
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    Multi-curve frameworks and information-based models
    (2024) Mahomed, Obeid; Taylor, David; Mc Walter Thomas
    The distinction between bank funding cash and derivative markets were magnified in the aftermath of the 2008 global financial crisis, and further fortified by the need for reference rate reform post the Financial Stability Board's review of major interest benchmarks in 2014. The cognisance of previously negligible liquidity and credit risks has had various implications for market microstructure and risk management. Accordingly, this has created the need for new interest rate modelling frameworks. Part I proposes one such framework, referred to as the “market-based approach”, which is a multi-curve generalisation of the single-curve pricing kernel approach, and is motivated by material differences that emerge due to term-related risks when executing compounding strategies at different frequencies. In this framework, a distinct stochastic discount factor is assigned to each tradable term within a given market. This term-cognisant approach is first applied to the deposit market, where a novel argument based on funding-swap duality and a constructed stylised systemic and symmetric setting enables the derivation of a system of arbitrage-free discrete-time calibrated pricing kernels. It is then shown how one may construct an exchange of risk mechanism to transfer risks across terms in a fair manner, which in turn enables economically meaningful and theoretically consistent pricing and valuation of financial instruments with features that span across terms. Finally, it is shown that the repo and bank funding markets are also compatible with the market-based approach, which paves the way for the development of derivative pricing and valuation. In Part II, the exchange of risk mechanism is generalised using a system of continuous-time pricing kernels and an FX analogy which results in the creation of the curve-conversion factor process. This process is then used to derive the across-curve pricing formula, which is a generalisation of the fundamental single pricing kernel formula, and defines the arbitrage-free mechanics of the “xy-approach” — a continuous-time reduced-form abstraction of the market-based approach. As a natural application, consistent multi-curve frameworks are formulated for bank funding cash and derivative markets within emerging and developed economies. Given the xy-approach, existing multi-curve frameworks based on HJM and rational pricing kernel models are recovered, reviewed, and generalised; and single-curve models are extended to a multicurve setting. In a final application, it is shown how the xy-approach offers a flexible framework for solving pricing problems involving financial instruments with floating nominal rate, inflation and foreign exchange exposures, in a consistent manner. Part III presents a reformulation of the information-based asset pricing framework, introduced by Macrina (2006), within a general non-linear stochastic filtering framework founded upon Markov observation and signal processes, in order to enhance tractability for model development. A general framework for modelling short, instantaneous forward, and discrete forward rates using pricing kernels is derived, which enables the creation of informatio