An algorithm for sequential tail value at risk for path-independent payoffs in a binomial tree

Abstract

We present an algorithm that determines Sequential Tail Value at Risk (STVaR) for path-independent payoffs in a binomial tree. STVaR is a dynamic version of Tail-Valueat-Risk (TVaR) characterized by the property that risk levels at any moment must be in the range of risk levels later on. The algorithm consists of a finite sequence of backward recursions that is guaranteed to arrive at the solution of the corresponding dynamic optimization problem. The algorithm makes concrete how STVaR differs from TVaR over the remaining horizon, and from recursive TVaR, which amounts to Dynamic Programming. Algorithmic aspects are compared with the cutting-plane method. Time consistency and comonotonicity properties are illustrated by applying the algorithm on elementary examples.

Time consistency of multi-period distortion measures

“…The set Q S is a polytope such that our sequentially consistent version of the multi-period distortion measure can be computed via linear programming. Roorda (2010) presents an algorithm for path-independent payoffs. To end this section, we want to explain why this acceptability measure is in general not dynamically consistent.…”

“…In this paper we also use the weaker consistency axioms of conditional and sequential consistency as introduced in Roorda and Schumacher (2007). To the best of our knowledge there is not much literature about conditionally consistent risk measures except for Roorda andSchumacher (2007, 2010). Roorda and Schumacher (2010) deduce that coherent risk measures can always be updated in a conditionally consistent way.…”

Some Approximate Results of Value-at-Risk for Dependent Compound Stochastic Sums of Heavy-Tailed Risks

“…The aim of this paper, however, is not primarily related to the controversy of value-at-risk vs. expected shortfall. For more details on Expected Shortfall with applications to stochastic models, we can refer to Roorda [30] and Biagini et al [19]. In addition, the introductions of copula theory can be found in Nelsen [31] and Panjer [21].…”