THE NONLINEAR ASYMMETRIC RELATIONSHIP AMONG IMPLIED VOLATILITY INDICES OF INDIAN STOCK MARKET, GOLD, AND OIL: EVIDENCE FROM NARDL MODEL

The paper aims to examine the nonlinear asymmetric relationship among the implied volatility indices of the Indian stock market, gold, and oil for the period from 2nd March 2009 to 29th October 2021. Nonlinear Autoregressive Distributed Lag (NARDL) model results provide evidence of asymmetric nonlinear relationship among the selected variables in the short-run and the long-run. The positive and negative shocks to gold and oil implied volatility indices have a positive and significant influence on the implied volatility of the Indian stock market. The expected volatility of gold has a short-term symmetric impact on expected stock market volatility in the short run. Whereas, the implied volatility of oil has a long-run asymmetric impact on the implied volatility of the stock market. Increasing volatility in oil prices can be viewed as a signal for the starting point for the volatility of the Indian stock markets. In the long run, positive shocks to gold volatility have more impact on the expected volatility of the Indian stock market than the negative. This indicates that investors are shifting their investments from gold to stocks for higher returns when the gold prices are fluctuating.

Option pricing with random risk aversion

Based on a standard general equilibrium economy, we develop a framework for pricing European options where the risk aversion parameter is state dependent, and aggregate wealth and the underlying asset have a bivariate transformed-normal distribution. Our results show that the volatility and the skewness of the risk aversion parameter change the slope of the pricing kernel, and that, as the volatility of the risk aversion parameter increases, the (Black and Scholes) implied volatility shifts upwards but its shape remains the same, which implies that the volatility of the risk aversion parameter does not change the shape of the risk neutral distribution. Also, we demonstrate that the pricing kernel may become non-monotonic for high levels of volatility and low levels of skewness of the risk aversion parameter. An empirical example shows that the estimated volatility of the risk aversion parameter tends to be low in periods of high market volatility and vice-versa.

Market expectation shifts in option-implied volatilities in the US and UK stock markets during the Brexit vote

This paper investigates the effect of the Brexit vote on the connection between UK stock market expectations and US stock market returns. To gauge UK stock market expectations, the option-implied volatilities of the FTSE 100 index are calculated in the period starting five months before and ending four months after the Brexit referendum. To keep the analysis “clean”, it stops right before the 2016 US presidential elections. It uses an OLS regression to estimate the change in the relationship between US and UK stock market expectations.The main findings show that the US and UK stock markets became somewhat less integrated four months after the Brexit referendum compared to the five months before it. The S&P 500 Index returns have a statistically significant impact on implied volatilities of the FTSE 100 only before the Brexit referendum. However, the British risk-free rate (LIBOR) became a statistically significant factor affecting FTSE 100 implied volatilities only after Brexit. This analysis may be used by decision-makers in the money management industry to act appropriately during Black Swan events. When UK citizens unexpectedly voted in favor of Brexit, the risk-free rate dropped, making it cheaper to invest, increasing the Sharpe ratios of equity portfolios. Coupled with increased uncertainty, this caused portfolio reallocations. In turn, expected volatility measured by options-implied volatility increased. AcknowledgmentThe authors would like to thank Olesia Verchenko for critique, a KSE M.A., external defense reviewer for helpful comments.

On the Quantitative Properties of Some Market Models Involving Fractional Derivatives

We review and discuss the properties of various models that are used to describe the behavior of stock returns and are related in a way or another to fractional pseudo-differential operators in the space variable; we compare their main features and discuss what behaviors they are able to capture. Then, we extend the discussion by showing how the pricing of contingent claims can be integrated into the framework of a model featuring a fractional derivative in both time and space, recall some recently obtained formulas in this context, and derive new ones for some commonly traded instruments and a model involving a Riesz temporal derivative and a particular case of Riesz–Feller space derivative. Finally, we provide formulas for implied volatility and first- and second-order market sensitivities in this model, discuss hedging and profit and loss policies, and compare with other fractional (Caputo) or non-fractional models.