In this paper, we address the problem of recovering the local volatility surface from option prices consistent with observed market data. We revisit the implied volatility problem and derive an explicit formula for the implied volatility together with bounds for the call price and its derivative...

Under discrete-time GARCH models markets are incomplete so there is more than one price kernel for valuing contingent claims. This motivates the quest for selecting an appropriate price kernel. Different methods have been proposed for the choice of a price kernel. Some of them can be justified...

In this paper we propose a type of mean reverting model with jumps, where the mean reverting level changes according to a continuous time, finite state Markov chain. This model could be applied to the interest rate and energy markets. We apply filtering techniques and obtain finite dimensional...

In this paper we develop a method for pricing derivatives under a Markov switching version of the Heston-Nandi GARCH (1, 1) model by using a well known tool from actuarial science, namely the Esscher transform. We suppose that the dynamics of the GARCH process switch over time according to one...

A Hidden Markov Chain (HMC) is applied to study the forward premium puzzle. The weekly quotient of the interest rate differential divided by the log exchange rate change is modeled as a Hidden Markov process. Compared with existing standard approaches, the Hidden Markov approach allows a...

We investigate the optimal investment timing strategy in a real option framework. Depending on the state of the economy, whose changes are modeled by a Markov chain, the investment cost can take one of two values. The optimal investment timing decision is determined by finding the free boundary...

The paper discusses the pricing of derivatives using a stochastic discount factor modeled as a regime switching geometric Brownian motion. The regime switching is driven by a continuous time hidden Markov chain representing changes in the economy. The stochastic discount factor enables to define...

It is known that the market in a Markovian regime-switching model is, in general, incomplete, so not all contingent claims can be perfectly hedged. We show, in this paper, how certain contingent claims are attainable in the regime-switching market using a money market account, a share and a...