On the market consistent valuation of fish farms: using the real option approach and salmon futures

We consider the optimal harvesting problem for a fish farmer in a model which accounts for stochastic prices featuring Schwartz (1997) two factor price dynamics. Unlike any other literature in this context, we take account of the existence of a newly established market in salmon futures, which determines risk premia and other relevant variables, that influence risk averse fish farmers in their harvesting decision. We consider the cases of single and infinite rotations. The value function of the harvesting problem determined in our arbitrage free setup constitutes the fair values of lease and ownership of the fish farm when correctly accounting for price risk. The data set used for this analysis contains a large set of futures contracts with different maturities traded at the Fish Pool market between 12/06/2006 and 22/03/2012. We assess the optimal strategy, harvesting time and value against two alternative setups. The first alternative involves simple strategies which lack managerial flexibility, the second alternative allows for managerial flexibility and risk aversion as modeled by a constant relative risk aversion utility function, but without access to the salmon futures market. In both cases, the loss in project value can be very significant, and in the second case is only negligible for extremely low levels of risk aversion. In consequence, for a risk averse fish farmer, the presence of a salmon futures market as well as managerial flexibility are highly important

Integration by Parts and Martingale Representation for a Markov Chain

Integration-by-parts formulas for functions of fundamental jump processes relating to a continuous-time, finite-state Markov chain are derived using Bismut's change of measures approach to Malliavin calculus. New expressions for the integrands in stochastic integrals corresponding to representations of martingales for the fundamental jump processes are derived using the integrationby-parts formulas. These results are then applied to hedge contingent claims in a Markov chain financial market, which provides a practical motivation for the developments of the integration-by-parts formulas and the martingale representations

The market for salmon futures: an empirical analysis of fish pool using the Schwartz multifactor model

Using the popular Schwartz 97 two-factor approach, we study future contracts written on fresh farmed salmon, which have been actively traded at the Fish Pool Market in Norway since 2006. This approach features a stochastic convenience yield for the salmon spot price. We connect this approach with the classical literature on fish-farming and aquaculture using first principles, starting by modeling the aggregate salmon farming production process and modeling the demand using a Cobb-Douglas utility function for a representative consumer. The model is estimated by means of Kalman filtering, using a rich data set of contracts with different maturities traded at Fish Pool between 12/06/2006 and 22/03/2012. The results are then discussed in the context of other commodity markets, specifically live cattle which acts as a substitute

On Reduced Form Intensity-based Model with Trigger Events

Corporate defaults may be triggered by some major market news or events such as financial crises or collapses of major banks or financial institutions. With a view to develop a more realistic model for credit risk analysis, we introduce a new type of reduced-form intensity-based model that can incorporate the impacts of both observable "trigger" events and economic environment on corporate defaults. The key idea of the model is to augment a Cox process with trigger events. Both single-default and multiple-default cases are considered in this paper. In the former case, a simple expression for the distribution of the default time is obtained. Applications of the proposed model to price defaultable bonds and multi-name Credit Default Swaps (CDSs) are provided

On Pricing Basket Credit Default Swaps

In this paper we propose a simple and efficient method to compute the ordered default time distributions in both the homogeneous case and the two-group heterogeneous case under the interacting intensity default contagion model. We give the analytical expressions for the ordered default time distributions with recursive formulas for the coefficients, which makes the calculation fast and efficient in finding rates of basket CDSs. In the homogeneous case, we explore the ordered default time in limiting case and further include the exponential decay and the multistate stochastic intensity process. The numerical study indicates that, in the valuation of the swap rates and their sensitivities with respect to underlying parameters, our proposed model outperforms the Monte Carlo method