Domenico De Giovanni

Pricing the Option to Surrender in Incomplete Markets

New international accounting standards require insurers to reflect the value of embedded options and guarantees in their products. Pricing techniques based on the Black and Scholes paradigm are often used; however, the hypotheses underneath this model are rarely met. We propose a framework that encompasses the most known sources of incompleteness. We show that the surrender option, joined with a wide range of claims embedded in insurance contracts, can be priced through our tool, and deliver hedging portfolios to mitigate the risk arising from their positions. We provide extensive empirical analysis to highlight the effect of incompleteness on the fair value of the option.

Time Charters with Purchase Options in Shipping: Valuation and Risk Management

The paper studies the valuation and optimal management of Time Charters with Purchase Options (T/C-POPs) which is a specific type of asset lease with embedded options that is common in shipping markets. T/C-POPs are economically significant and sometimes account for more than half of the stock market value of listed shipping companies. The main source of risk in markets for maritime transportation is the freight rate, and we therefore specify a single-factor continuous time model for the dynamic evolution of freight rates which allows us to price a wide variety of freight rate related derivatives including various forms of T/C-POPs using contingent claims valuation techniques. Our model allows for the derivation of closed valuation formulas for some simple freight rate derivatives while the more complex ones are analyzed using numerical (finite difference) procedures. We accompany our theoretical results with illustrative numerical examples as we proceed

Delta hedging strategies comparison

Abstract In this paper we implement dynamic delta hedging strategies based on several option pricing models. We analyze different subordinated option pricing models and we examine delta hedging costs using ex-post daily prices of S&P 500. Furthermore, we compare the performance of each subordinated model with the Black–Scholes model.

Dynamic Harvesting Under Imperfect Catch Control

We analyze the optimal harvesting rule of a monopolist in a managed single-species fishery environment where we allow the fishery control to be imperfect. The monopolist’s control action consists of legal and illegal actions. Illegal actions might be detected at random times, in which case the monopolist is subject to a deterrence scheme in line with the Common Fishery Policy implemented by the European Union. We show that the introduction of the management policy, together with the inability of the regulator to perfectly monitor fishing activities, creates an incentive to harvest not only beyond the allowed quota, but also beyond the harvest in an unregulated but otherwise equal situation. This effect is particularly pronounced at lower levels of the legal quota. We also show that, if the monopolist is sufficiently impatient, over-harvesting with severe depletion of the resource might even occur under a reinforced deterrence scheme that considers the permanent withdrawal of the fishing license.

Pricing Reinsurance Contracts

Pricing and hedging insurance contracts is hard to perform if we subscribe to the hypotheses of the celebrated Black and Scholes model. Incomplete market models allow for the relaxation of hypotheses that are unrealistic for insurance and reinsurance contracts. One such assumption is the tradeability of the underlying asset. To overcome this drawback, we propose in this chapter a stochastic programming model leading to a superhedging portfolio whose final value is at least equal to the insurance final liability. A simple model extension, furthermore, is shown to be sufficient to determine an optimal reinsurance protection for the insurer: we propose a conditional value at risk (VaR) model particularly suitable for large-scale problem instances and rationale from a risk theoretic point of view.