Pricing Approaches for Guaranteed Annuity Options
This is an excerpt from the paper...
This study investigates pricing approaches for guaranteed annuity options. The study focuses on the comparative accuracy of alternative approaches to the pricing of guaranteed annuity options.The payout from many insurance contracts depends in some way upon the actual investment return earned on the assets subject to some minimum guarantee. Payouts may depend on the investment return in one of two ways. First, with unit-linked policies, the payout is directly linked to the performance of the underlying assets. Second, with participation policies, policy owners share the profits of the insurer. The full effect of the investment return is not immediately credited to participating policies. Rather, a series of bonuses is declared which will smooth the return credited to the policies. The guarantee of returns may be structured in a variety of ways. The most common structural forms are as follows: 1. Maturity Guarantee: In a maturity guarantee, the return is guaranteed on maturity of the policy. A return is not guaranteed in the case of an early surrender of the policy. 2. Surrender Guarantee: In a surrender guarantee structure, the guaranteed policy value can be claimed by the policy holder at any time up to and including maturity. The guaranteed amount tends to increase as the time of surrender approaches the policy term. 3. Guaranteed Annuity Option: With a guaranteed annuity option, the payout at ma
. . .
áááááááááááááááááSD(t)+ á
d2 ááá= d1 - [SD(t)+]; á
áááááááwhere: á
ááááááááááIn(Ps/E) = the natural log of (Ps/E); á
SD ááá= the standard deviation of the annual ááááááááááááááááááááááááááááááááááááááárate of return on the underlying stock.
All of the data required for the Black-Scholes model are readily available. áThis availability of data makes use of the model feasible. áAs the illustration of the model indicates, the distribution of stock price variances is a major assumption built into the formula. á
Replicating Portfolio Techniques
The payoff from many derivatives, including options, can be replicated by portfolios of other assets whose prices are known. Within the context of the no arbitrage principle, the price of the derivative must be equal to the value of the assets in the replicating portfolio. The process is equivalent to calculating the expected present value of the payoff at the risk-free rate of return. The expectation, however, is not calculated using the real world probabilities of the payoffs. Rather, the expectation is calculated using the equivalent martingale measure. The equivalent martingale concept holds that the inevitability of dynamic hedging and the uniqueness of the dynamic hedging str
. . .
Some common words found in the essay are:
Brealey Myers, Diaz Skinner, Boyle Hardy, Vollet Bousset, Hull White, CAPM Common, PsNd1 Eantiln, Solutions Derivative, SPV SPV, Hui Lo, credit derivatives, guaranteed annuity, credit derivative, default risk, guaranteed annuity options, sharpe 1999, annuity options, structural models, reduced form, annuity option, credit default, guaranteed annuity option, diaz skinner 2001, pricing credit derivatives, credit derivative instrument,
Approximate Word count = 6695
Approximate Pages = 27 (250 words per page)
|