Valuation of Insurance Products with Shout Options in a Jump-Diffusion Model

The insurance product with shout options which permit the holders to modify the contract rules is one of the most popular products in European and American markets today. Therefore, it is of great significance to price more precisely. A new mathematical model consisting of a partial differential inequality and constraint conditions is derived for the price of insurance products in a jump-diffusion model. The numerical experiments are performed to analyze the impact of parameters on the insurance product with shout put options, especially for the jump times and the quantities of shout opportunities. The experiment results show that the value of the product is strongly affected by the quantities of shouting opportunities, especially for high values of the underlying asset, while it is only weakly affected for low values. Meanwhile, another meaningful discovery is that the valuation has changed little as the jump times are less than five, while it has shown a sharp increase once the jump times are more than five. Furthermore, the indicator results of course grid errors show that the values of shout put options in the jump-diffusion model are more accurate than those in a Brownian motion.

Risk-Neutral Pricing Method of Options Based on Uncertainty Theory

In order to rationally deal with the belief degree, Liu proposed uncertainty theory and refined into a branch of mathematics based on normality, self-duality, sub-additivity and product axioms. Subsequently, Liu defined the uncertainty process to describe the evolution of uncertainty phenomena over time. This paper proposes a risk-neutral option pricing method under the assumption that the stock price is driven by Liu process, which is a special kind of uncertain process with a stationary independent increment. Based on uncertainty theory, the stock price’s distribution and inverse distribution function under the risk-neutral measure are first derived. Then these two proposed functions are applied to price the European and American options, and verify the parity relationship of European call and put options.

Efficient Variance Reduction for American Call Options Using Symmetry Arguments

Recently it was shown that the estimated American call prices obtained with regression and simulation based methods can be significantly improved on by using put-call symmetry. This paper extends these results and demonstrates that it is also possible to significantly reduce the variance of the estimated call price by applying variance reduction techniques to corresponding symmetric put options. First, by comparing performance for pairs of call and (symmetric) put options for which the solution coincides, our results show that efficiency gains from variance reduction methods are different for calls and symmetric puts. Second, control variates should always be used and is the most efficient method. Furthermore, since control variates is more effective for puts than calls, and since symmetric pricing already offers some variance reduction, we demonstrate that drastic reductions in the standard deviation of the estimated call price is obtained by combining all three variance reduction techniques in a symmetric pricing approach. This reduces the standard deviation by a factor of over 20 for long maturity call options on highly volatile assets. Finally, we show that our findings are not particular to using in-sample pricing but also hold when using an out-of-sample pricing approach.

On the feasibility of reverse mortgages in Colombia

Purpose The Colombian Government proposed a reverse mortgage mechanism to complement retirement income in Colombia. This paper aims to study its feasibility by valuing its premia. Design/methodology/approach Under a reverse mortgage scheme, banks issue put options on an owner’s home. To value the option, the authors apply a risk-neutral canonical approach modeling its three sources of risk: home future value, interest rate levels and homeowner life expectancy. Findings In all, premia values do not seem too high. However, if future interest rates are above the simulations or home appreciation is below its historical behavior, the premia could sharply increase, jeopardizing the system viability. Limiting the loan-to-home-value ratio or fixed-term annuities are feasible alternatives to keep premium increases at bay. Complementary mechanisms may also help. Research limitations/implications The home price and interest rate path estimation do not include inflation dynamics; in recent years inflation level was very low. However, the future does not offer any warrants. Future research also should cap the maximum loss the bank can endure. The pandemic may cause demographic changes affecting the viability of the reverse mortgage (R.M.) program in Colombia. Practical implications Based on the analysis, this work suggests possible government policies to help creditors and to maintain bank risks at a reasonable level. Social implications An adequate reverse mortgage program may help the policymakers in Colombia to face the adverse environment for Colombia’s housing market and the pressure of its pension system. A good R.M. program generates incentives to purchase homes, given the possibility of receiving an additional rent after retirement. Originality/value The paper develops an econometrical improvement over previous work. The authors present a time-series analysis that includes stationarity and co-integration information to model the data-generation process of house prices and interest rates in a multivariate fashion. The authors also improve the valuation formula. Moreover, the paper presents a novel application to Colombia. The authors obtain our demographic data from the United Nations Population Division applying the Lee-Carter method to model mortality rates, which provides ample possibilities to extend reverse mortgage assessment to additional. Finally, this is the first scholarly effort to evaluate the R.M. for the Colombian case.

The Profitability of Volatility Trading on Exchange-traded Dollar-rupee Options: Evidence of a Volatility Risk Premium?

This article examines the profitability of short volatility strategies in the exchange-traded USDINR options market. Returns from delta-hedged short positions in straddles, strangles and individual call and put options are examined across different trading horizons and volatility regimes. The study finds that short volatility strategies yield significant mean and median returns regardless of the trading horizon and option moneyness before considering transaction costs. This is suggestive of a volatility risk premium priced in USDINR options. However, the returns are found to be insignificant and even negative after accounting for trading costs such as bid-ask spreads and brokerage. The study concludes that although USDINR options appear to be overpriced because of the volatility risk premium, short option strategies can be profitably exploited only by market makers and institutional investors facing low spreads and funding costs. The findings are suggestive of an informationally efficient market.

Hedging the Price Risk Inherent in Revenue Protection Insurance

Crop revenue insurance is unique, because it involves a guarantee subsuming yield risk and highly systematic price risk. This study examines whether crop insurers could use options instead of, or in addition to, assigning policies to the Commercial Funds of the USDA Federal Crop Insurance Corporation (FCIC) as per the Standard Reinsurance Agreement (SRA) to hedge the price risk of revenue insurance policies. The behavioral model examines the optimal hedge ratio for a crop insurer with a book of business consisting of corn Revenue Protection (RP) policies. Results show that a mix of put and call options can hedge the price risk of the RP policies. The higher optimal hedge ratios of call options as compared to put options imply that the risk of increased liability due to upside price risk can be hedged using options better than downside price risk. This study also analyzed the combination of options with the SRA at 35, 50, and 75% retention levels. The zero optimal hedge ratios at each retention level and the negative correlation between RP indemnities and the option returns when the crop insurer mixed options and SRA suggest that the purchasing of options provides no additional risk protection to crop insurers beyond what is provided by the SRA despite retention limits.

Option Pricing, Zero Lower Bound, and COVID-19

This paper provides a quantitative assessment of equity options priced at the Zero Lower Bound, i.e., when interest rates are set essentially to zero. We obtain closed form formulas for American options when the Zero Lower Bound policy holds. We perform numerical implementation of American put options written on the stock Federal National Mortgage Association (FNMA) and of related bounds for the optimal exercise. The results show similarities with the corresponding European options priced at the Zero Lower Bound during the COVID-19 crisis.

Optimal Pricing and Ordering Strategies with a Flexible Return Strategy under Uncertainty

To coordinate the supply chain risk caused by demand uncertainty, this paper proposed a flexible return strategy under demand uncertainty, in which the retailer can choose return quantity independently by put option after the selling season, while the return quantity is usually determined by the supplier in the classical return strategy. In our novel return strategy, the exercise price is not fixed, and we developed the base model of this strategy, named the selective buyback contracts model. We have solved the optimal pricing and ordering strategies of supply chain members. Numerical studies demonstrated that the contracts can coordinate a supply chain with one retailer and one supplier, and the supplier can adjust the profit distribution of the supply chain by adjusting the option exercise price. Compared with other return strategies, the selective buyback contracts give the retailer more power of choice, and the supplier receives risk compensation from the put options.