The volatility structure of 90-day bill futures traded on the Sydney Futures Exchange is analysed within the framework of the Heath-Jarrow-Morton model. The method involves characterisation of the transition probability density function for the forward rate process represented by the stochastic differential equation in the arbitrage-free economy. Maximisation of the likelihood function then res...

This paper consists in introducing an option price expansion for model combining local and stochastic volatility with tight error estimates. The local volatility part is considered as general but has to satisfy some growth and boundedness assumptions. For the stochastic part, we choose a square root process, which is usually used for modelling the behaviour of the variance process. In the parti...

We develop a discrete-time stochastic volatility option pricing model, which exploits the information contained in high-frequency data. The Realized Volatility (RV) is used as a proxy of the unobservable log-returns volatility. We model its dynamics by a simple but effective (pseudo) long-memory process, the Leverage Heterogeneous Auto-Regressive Gamma (HARGL) process. Both the discrete-time sp...

A multivariate stochastic volatility model with dynamic equicorrelation and cross leverage effect is proposed and estimated. Using a Bayesian approach, an efficient Markov chain Monte Carlo algorithm is described where we use the multi-move sampler, which generates multiple latent variables simultaneously. Numerical examples are provided to show its sampling efficiency in comparison with the si...

This paper introduces a new methodology for measuring and analyzing capital structure effects on option prices of individual firms in the economy. By focusing on individual firms we examine the cross sectional effects of leverage on option prices. Our methodology allows the market value of each firm’s debt to be implied directly from two contemporaneous, liquid, at-the-money option prices witho...

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 describe some stochastic control problems in financial engineering arising from the need to find investment strategies to optimize some goal. Typically, these problems are characterized by nonlinear Hamilton-Jacobi-Bellman partial differential equations, and often they can be reduced to linear PDEs with the Legendre transform of convex duality. One situation where this cannot be achieved is ...

This paper introduces a no-arbitrage framework to assess how macroeconomic factors help explain the risk-premium agents require to bear the risk of fluctuations in stock market volatility. We develop a model in which return volatility and volatility risk-premia are stochastic and derive no-arbitrage conditions linking volatility to macroeconomic factors. We estimate the model using data related...

Stochastic volatility determines, as a rule, the extreme risk in price fluctuations. We review some of the most important stochastic volatility models concerning their extreme behaviour. This includes the tail behaviour as well as the cluster possibilities of such models. The following pattern is common for discretetime and continuous-time models. In linear models the volatility inherits the ta...

Simulated maximum likelihood has proved to be a valuable tool for fitting the log-normal stochastic volatility model to financial returns time series. In this paper, we develop a methodology that generalizes these methods to more general stochastic volatility models that are naturally cast in terms of a positive volatility process. The methodology relies on combining two well known methods for ...