The Impact of Overnight Periods on Option Pricing

Abstract

This paper investigates the effect of closed overnight exchanges on option prices. During the trading day, asset prices follow the literature's standard affine model that allows for stochastic volatility and random jumps. Independently, the overnight asset price process is modeled by a single jump. We find that the overnight component reduces the variation in the random jump process significantly. However, neither the random jumps nor the overnight jumps alone are able to empirically describe all features of option prices. We conclude that both random jumps during the day and overnight jumps are important in explaining option prices, where the latter account for about one quarter of total jump risk.

The price-setting behavior of banks: An analysis of open-end leverage certificates on the German market

“…To analyze how the presence of gap risk affects our findings on the valuation of OELCs in Section 4, we replace here the dynamics of the underlying under the risk-neutral measure (see (8)) with a jump-diffusion process which incorporates random and overnight jumps separately according to Boes et al (2007): 19…”

“…From the investor's perspective (which is not the focus of this paper), default-free OELCs are certainly more valuable to them than OELCs with default risk if we assume investors expect benefits from investing in and holding OELCs. 19 Boes et al (2007) additionally allow for stochastic volatility which we here ignore to reduce the calculation burden when calibrating the process. Câmara (2008) proposes a model with two counters of random jumps.…”

“…Taylor (2007) shows how to incorporate overnight information to better estimate conditional volatilities. 20 This specification implies that, given a random jump occurs, the expected (jump) stock return is l RJ , whereas daily jumps do not change the stock price in expectation, see Boes et al (2007).…”

“…This is a natural approach since there is evidence in the literature that jump risk, besides stochastic volatility, causes the volatility smile (e.g., Bakshi et al, 1997;Pan, 2002;Boes et al, 2007). At each trading day we consider the price of the last trade of each put option with a remaining time to maturity of up to one year.…”

Overnight information and stochastic volatility: A study of European and US stock exchanges

“…More recently, Taylor (2007) evaluates the predictive ability of overnight trading in the E-mini S&P 500 futures market and demonstrates that volatility forecasts produced by models that incorporate overnight information can lead to more accurate Value-at-Risk measures. Finally, Boes et al (2007) examine the impact of overnight periods on option prices and find that overnight jumps account for one quarter of the total jump variance. However, a common thread of these studies is that: (i) they do not explicitly model the predictive ability of overnight information in both daytime stock returns and volatility, and (ii) they do not distinguish between the four nontrading periods of weeknights, weekends, holidays and long weekends.…”