Abstract
This paper provides a discrete-time approach for evaluating financial and actuarial products characterized by path-dependent features in a regime-switching risk model. In each regime, a binomial discretization of the asset value is obtained by modifying the parameters used to generate the lattice in the highest-volatility regime, thus allowing a simultaneous asset description in all the regimes. The path-dependent feature is treated by computing representative values of the path-dependent function on a fixed number of effective trajectories reaching each lattice node. The prices of the analyzed products are calculated as the expected values of their payoffs registered over the lattice branches, invoking a quadratic interpolation technique if the regime changes, and capturing the switches among regimes by using a transition probability matrix. Some numerical applications are provided to support the model, which is also useful to accurately capture the market risk concerning path-dependent financial and actuarial instruments.
Highlights
With the aim of providing an accurate evaluation of the risks affecting financial markets, a wide range of empirical research evidences that asset returns show stochastic volatility patterns and fatter tails with respect to the standard normal model
We develop an algorithm to evaluate financial and actuarial products characterized by path-dependent features and manage the market risk concerning such products
This paper contributes to the literature in three main ways: it presents a simple binomial lattice algorithm when the underlying asset dynamics is described by a regime-switching model, which is useful for practitioners to evaluate financial and actuarial products characterized by path-dependent features and to manage the market risk concerning such products; the model reduces the computational complexity by working on actual paths of a binomial lattice and overcomes the drawbacks evidenced above for the Yuen and Yang (2010) method; the proposed lattice approach is characterized by the relevant feature of being flexible in that different specifications of the path-dependent function may be managed in the developed model, and it is clearly suitable for managing both European and American-style products under regime-switching
Summary
With the aim of providing an accurate evaluation of the risks affecting financial markets, a wide range of empirical research evidences that asset returns show stochastic volatility patterns and fatter tails with respect to the standard normal model. Hamilton (1989), (1990) introduces regime-switching models that represent simple tools to capture the stochastic volatility behaviour and, fat tails These models overcome the problems affecting the Black and Scholes (1973) framework, characterized by a constant volatility level, by allowing the financial parameters to assume different values in different time periods following a process that generates switches among regimes. Empirical evidence supporting these models shows that they capture more accurately the stylized facts of financial returns and provide a useful and more precise instrument for risk management, a fundamental activity in the modern financial and actuarial world. To name just a few, examples are provided firstly in Bollen et al (2000) and, later, in
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