Dumas, Fleming, Whaley (DFW, 1998) find that option models based on deterministic volatility functions (DVF) perform poorly because the estimated volatility function is unstable over time. DFW provide evidence that the DVF changes significantly on a weekly basis. This paper proposes a new class of dynamic implied volatility function models (DIVF). This class of models separates a time-invariant...

In this paper we extend the standard binomial model to obtain a more flexible model that will be calibrated with market data on European puts and calls. We also discuss how this extended model can be used to incorporate an investor’s view of the future behaviour of the stock market.

We address the problem of defining and calculating forward volatility implied by option prices when the underlying asset is driven by a stochastic volatility process. We examine alternative notions of forward implied volatility and the information required to extract these measures from the prices of European options at fixed maturities. We then specialize to the SABR model and show how the asy...

Basic: linear inequalities containing only current accumulator values (i.e. ci≥0) History Variables: number of previous accumulator values (i.e. ci-2+1≥ci) State Variable: include a variable q representing the current state (i.e. ci-ci-1≤q) State Specific Implied Constraints: generate ICs that hold at specific states (i.e. q=s ⇒ ci=ci-1) Index Variable: include the current index (i.e. 2ci≤i) Ex...

This paper presents a deterministic numerical method to calculate the implied volatility of an option based on multiple assets using a stochastic volatility model. The approach uses Varadhan asymptotics for the diffusion kernel and involves the constrained minimization of a numerically computed geodesic length. We produce implied volatilities for baskets with 10 – 50 elements using the SABR sto...

We study asymptotics of forward-start option prices and the forward implied volatility smile using the theory of sharp large deviations (and refinements). In Chapter 1 we give some intuition and insight into forward volatility and provide motivation for the study of forward smile asymptotics. We numerically analyse no-arbitrage bounds for the forward smile given calibration to the marginal dist...

We examine the small expiry behaviour of the price of call options in models of exponential Lévy type. In most cases of interest, it turns out that E ( (Sτ −K) ) − (S0 −K) ∼ { τ ∫ R (S0e x −K)+ ν(dx), S0 < K, τ ∫ R (K − S0e) ν(dx), S0 > K, as τ → 0+, i.e. as time to expiry goes to zero. (We have written ν for the Lévy measure of the driving Lévy noise.) In “complete generality”, however, we can...

Phylogenetic relationships within the “symmetrical” hermit crab family Pylochelidae were analyzed for 41 of the 45 species and subspecies currently considered valid. In the analyses, 78 morphological characters comprised the data matrix and the outgroup consisted of Thalassina anomala, a member of the Thalassinidae, and Munida quadrispina, a member of the Galatheidae. A poorly resolved strict c...