EFFICIENT HEDGING FOR DEFAULTABLE SECURITIES AND ITS APPLICATION TO EQUITY-LINKED LIFE INSURANCE CONTRACTS

2015 ◽  
Vol 18 (07) ◽  
pp. 1550047
Author(s):  
ALEXANDER MELNIKOV ◽  
AMIR NOSRATI
Keyword(s):  
Life Insurance ◽  
Closed Form Solution ◽  
Form Solution ◽  
Recovery Rates ◽  
Insurance Contracts ◽  
Black Scholes ◽  
Simple Alternative ◽  
Defaultable Securities ◽  
Efficient Hedging ◽  
Hedging Problem

The paper deals with efficient hedging problem for defaultable securities with multiple default times and nonzero recovery rates. First, we convert the efficient hedging problem into a Neyman–Pearson problem with composite hypothesis against a simple alternative. Then we apply nonsmooth convex duality to provide a solution in the framework of a “defaultable” Black–Scholes model. Moreover, in the case of zero recovery rates, we find a closed form solution for the problem. As an application, it is shown how to use such type of results in pricing equity-linked life insurance contracts. The results are also demonstrated by some numerical examples.

A Closed-Form Solution for the Global Quadratic Hedging of Options under Geometric Gaussian Random Walks

2019 ◽  
Keyword(s):  
Closed Form ◽  
Recursive Algorithm ◽  
Closed Form Solution ◽  
Form Solution ◽  
Closed Form Expression ◽  
Problem Solution ◽  
Underlying Asset ◽  
Quadratic Hedging ◽  
Hedging Problem ◽  
The Impact

This study obtains a closed-form solution for the discrete-time global quadratic hedging problem of Schweizer (1995) applied to vanilla European options under the geometric Gaussian random walk model for the underlying asset. This extends the work of Rémillard and Rubenthaler (2013), who obtained closed-form formulas for some components of the hedging problem solution. Coefficients embedded in the closed-form expression can be computed either directly or through a recursive algorithm. The author also presents a brief sensitivity analysis to determine the impact of the underlying asset drift and the hedging portfolio rebalancing frequency on the optimal hedging capital and the initial hedge ratio.

On the Risk-Neutral Valuation of Life Insurance Contracts with Numerical Methods in View

2010 ◽  
Vol 40 (1) ◽  
pp. 65-95 ◽  
Author(s):  
Daniel Bauer ◽  
Daniela Bergmann ◽  
Rüdiger Kiesel
Keyword(s):  
Life Insurance ◽  
Insurance Companies ◽  
Generic Model ◽  
Model Risk ◽  
Early Exercise ◽  
Insurance Contracts ◽  
Black Scholes ◽  
Market Consistent Valuation ◽  
The Impact ◽  
Valuation Of Life

AbstractIn recent years, market-consistent valuation approaches have gained an increasing importance for insurance companies. This has triggered an increasing interest among practitioners and academics, and a number of specific studies on such valuation approaches have been published.In this paper, we present a generic model for the valuation of life insurance contracts and embedded options. Furthermore, we describe various numerical valuation approaches within our generic setup. We particularly focus on contracts containing early exercise features since these present (numerically) challenging valuation problems.Based on an example of participating life insurance contracts, we illustrate the different approaches and compare their efficiency in a simple and a generalized Black-Scholes setup, respectively. Moreover, we study the impact of the considered early exercise feature on our example contract and analyze the influence of model risk by additionally introducing an exponential Lévy model.

scholarly journals Option Pricing And Monte Carlo Simulations

2011 ◽  
Vol 3 (9) ◽  
Author(s):  
George M. Jabbour ◽  
Yi-Kang Liu
Keyword(s):  
Monte Carlo ◽  
Option Pricing ◽  
Monte Carlo Simulations ◽  
Variance Reduction ◽  
Closed Form Solution ◽  
Form Solution ◽  
Price Convergence ◽  
Option Prices ◽  
Black Scholes ◽  
The Difference

The advantage of Monte Carlo simulations is attributed to the flexibility of their implementation. In spite of their prevalence in finance, we address their efficiency and accuracy in option pricing from the perspective of variance reduction and price convergence. We demonstrate that increasing the number of paths in simulations will increase computational efficiency. Moreover, using a t-test, we examine the significance of price convergence, measured as the difference between sample means of option prices. Overall, our illustrative results show that the Monte Carlo simulation prices are not statistically different from the Black-Scholes type closed-form solution prices.

scholarly journals EFFICIENT HEDGING AND PRICING OF EQUITY-LINKED LIFE INSURANCE CONTRACTS ON SEVERAL RISKY ASSETS

2008 ◽  
Vol 11 (03) ◽  
pp. 295-323 ◽  
Author(s):  
ALEXANDER MELNIKOV ◽  
YULIYA ROMANYUK
Keyword(s):  
Life Insurance ◽  
Financial Risk ◽  
Risk Preference ◽  
Financial Assets ◽  
Insurance Risk ◽  
Risky Assets ◽  
Insurance Contracts ◽  
Maturity Date ◽  
Efficient Hedging ◽  
Probabilistic Result

The paper uses the efficient hedging methodology in order to optimally price and hedge equity-linked life insurance contracts whose payoff depends on the performance of several risky assets. In particular, we consider a policy which pays the maximum of the values of n risky assets at some maturity date T, provided that the policyholder survives to T. Such contracts incorporate financial risk, which stems from the uncertainty about future prices of the underlying financial assets, and insurance risk, which arises from the policyholder's mortality. We show how efficient hedging can be used to minimize expected losses from imperfect hedging under a particular risk preference of the hedger. We also prove a probabilistic result, which allows one to calculate analytic pricing formulas for equity-linked payoffs with n risky assets. To illustrate its use, explicit formulas are given for optimal prices and expected hedging losses for payoffs with two risky assets. Numerical examples highlighting the implications of efficient hedging for the management of financial and insurance risks of equity-linked life insurance policies are also provided.

OPTION BETAS: RISK MEASURES FOR OPTIONS

2007 ◽  
Vol 10 (07) ◽  
pp. 1137-1157 ◽  
Author(s):  
NICOLE BRANGER ◽  
CHRISTIAN SCHLAG
Keyword(s):  
Asset Pricing ◽  
Risk Measures ◽  
Risk Measure ◽  
Closed Form Solution ◽  
Form Solution ◽  
Option Prices ◽  
Time Intervals ◽  
Return Interval ◽  
Black Scholes ◽  
The Impact

This paper deals with the problem of determining the correct risk measure for options in a Black–Scholes (BS) framework when time is discrete. For the purposes of hedging or testing simple asset pricing relationships previous papers used the "local", i.e., the continuous-time, BS beta as the measure of option risk even over discrete time intervals. We derive a closed-form solution for option betas over discrete return periods where we distinguish between "covariance betas" and "asset pricing betas". Both types of betas involve only simple Black–Scholes option prices and are thus easy to compute. However, the theoretical properties of these discrete betas are fundamentally different from those of local betas. We also analyze the impact of the return interval on two performance measures, the Sharpe ratio and the Treynor measure. The dependence of both measures on the return interval is economically significant, especially for OTM options.

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