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.

Pricing Multivariate European Equity Option Using Gaussians Mixture Distributions and EVT-Based Copulas

In this article, we present an approach which allows taking into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associated options. Specifically, the marginal distribution of asset returns is modelled by a mixture of two Gaussian distributions. Moreover, we model the joint dependence structure of the returns using a copula function, the extremal one, which is suitable for our financial data, particularly the extreme values copulas. Applications are made on the Atos and Dassault Systems actions of the CAC40 index. Monte Carlo method is used to compute the values of some equity options such as the call on maximum, the call on minimum, the digital option, and the spreads option with the basket (Atos, Dassault systems) as underlying.

A closed-form pricing formula for catastrophe equity options

In this article, we derive a closed-form pricing formula for catastrophe equity put options under a stochastic interest rate framework. A distinguishing feature of the proposed solution is its simplified form in contrast to several recently published formulae that require evaluating several layers of infinite sums of $n$ -fold convoluted distribution functions. As an application of the proposed formula, we consider two different frameworks and obtain the closed-form formula for the joint characteristic function of the asset price and the losses, which is the only required ingredient in our pricing formula. The prices obtained by the newly derived formula are compared with those obtained using Monte-Carlo simulations to show the accuracy of our formula.

Closed-form pricing formula for foreign equity option with credit risk

Since credit risk in the over-the-counter (OTC) market has undoubtedly become very important issue, credit risk has to be considered when the options in the OTC market are priced. In this paper, we consider the valuation of foreign equity options with credit risk. In order to derive a closed-form pricing formula of this option, we adopt the partial differential equation (PDE) approach and use the Mellin transform method to solve the PDE. Specifically, triple Mellin transforms are used, and the pricing formula is presented as 3-dimensional normal cumulative distribution functions. Finally, we verify that our closed-form formula is accurate by comparing it with the numerical result from the Monte-Carlo simulation.

Stock Return Autocorrelation and Individual Equity Option Prices

This study demonstrates empirically the impact of stock return autocorrelation on the prices of individual equity option. The option prices are characterized by the level and slope of implied volatility curves, and the stock return autocorrelation is measured by variance ratio and first-order serial return autocorrelation. Using a large sample of U.S. stocks, we show that there is a clear link between stock return autocorrelation and individual equity option prices: a higher stock return autocorrelation leads to a lower level of implied volatility (compared to realized volatility) and a steeper implied volatility curve. The stock return autocorrelation is more important in explaining the level of implied volatility curve for relatively small stocks. The relation between stock return autocorrelation and option price structure is more pronounced when market is volatile, especially during financial crisis. The stock return autocorrelation is more important in explaining the level of implied volatility curve for relatively small stocks. Thus, stock return autocorrelation can help differentiate the price structure across individual equity options.

Ideal Investment Protection in Optimistic Perceptions: Evidence From the Indian Equity Options Market

The study is an experiential assessment on the ability of the Indian equity options market to resist the adverse impacts that arise from unexpected changes in the underlying equity market, focusing on two distinct investor perceptions within optimistic dimension in the market, viz. the recovery phase and the growth phase, which were evident in the Indian market scenario post the period of financial upheavals due to global economic crisis during the latter half of 2000s. The risk mitigation capability of the options is examined in terms of long run integration and short run re-equilibrating relationship shown by near month calls and puts with varied stages of exercisability with their underlying equity segment in the National Stock Exchange of India. Further, the ideal hedge sizes of the options and the hedge gains resulting from affecting them in the investment profile are identified under minimum variance framework, using Diagonal BEKK GARCH. The results are indicative that all different options segments express to have the expected resistance ability during both bullish perceptions under consideration, and prove that optimal use of options with equity portfolio provides assured hedge gains in terms of reduction in un-anticipatable variances.

Information Content of Aggregate Implied Volatility Spread

Aggregate implied volatility spread (IVS), defined as the cross-sectional average difference in the implied volatilities of at-the-money call and put equity options, is significantly and positively related to future stock market returns at daily, weekly, and monthly to semiannual horizons. This return predictive power is incremental to existing return predictors, and it is significant both in sample and out of sample. Furthermore, IVS can forecast macroeconomic news up to one year ahead. The return predictability concentrates around macro news announcement. Common informed trading in equity options offers an integrated explanation for the ability of IVS to predict both future stock market returns and real economic activity. This paper was accepted by Tyler Shumway, finance.

Is Indian Equity Options Market Suitable for Hedging When the Options Payoff Structure Changes?

Investments are essential as the growth of the stock market denoted through increased investments results in the growth of the economy. But they are always subject to various risks in the market. These risks are to be mitigated for the development of an efficient economic system by the market itself. Apart from the stock segment, the Indian financial market is a home for futures and options segments that facilitate the hedging of risks involved in the investments. For considering any derivative market as a hedging tool, one of the prerequisites is the presence of integration between such derivative market and its underlying market. The present study focuses on testing the relationship between Indian stock market and the options market, represented by NSE Nifty 50 index and index options on it respectively, to know whether the options segment is suitable for hedging the risks implicit with investments in the stock market, with substantial consideration to payoff structure of the market denoted by different moneyness groups viz.