Related papers: Leveraged {ETF} implied volatilities from {ETF} dy…
Daily leveraged exchange traded funds amplify gains and losses of their underlying benchmark indexes on a daily basis. The result of going long in a daily leveraged ETF for more than one day is less clear. Here, bounds are given for the…
Exchange Traded Funds (ETFs) have been gaining increasing popularity in the investment community as is evidenced by the high growth both in the number of ETFs and their net assets since 2000. As ETFs are in nature similar to index mutual…
The measures of roughness of the volatility in the litterature are based on the realized volatility of high frequency data. Some authors show that this leads to a biased estimate, and does not necessarily indicate roughness of the…
This paper estimates the carry embedded in listed IBIT options and compares it with the carry embedded in matched CME bitcoin futures. Put-call parity recovers an implied forward on the ETF; BlackRock's daily holdings file maps each ETF…
In this paper similar to [P. Carr, A. Itkin, 2019] we construct another Markovian approximation of the rough Heston-like volatility model - the ADO-Heston model. The characteristic function (CF) of the model is derived under both…
In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlying's return, whereas gradual changes in implied volatility…
This study investigates the short-term asymptotic behavior of the implied volatility surface (IVS), with a particular focus on the at-the-money (ATM) skew and curvature, which are key determinants of the IVS shape and whose are widely…
We study specific nonlinear transformations of the Black-Scholes implied volatility to show remarkable properties of the volatility surface. Model-free bounds on the implied volatility skew are given. Pricing formulas for the European…
It is known that the implied volatility skew of FX options demonstrates a stochastic behavior which is called stochastic skew. In this paper we create stochastic skew by assuming the spot/instantaneous variance correlation to be stochastic.…
We present an option pricing formula for European options in a stochastic volatility model. In particular, the volatility process is defined using a fractional integral of a diffusion process and both the stock price and the volatility…
This paper studies the empirical tracking performance of leveraged ETFs on gold, and their price relationships with gold spot and futures. For tracking the gold spot, we find that our optimized portfolios with short-term gold futures are…
The coupled nonlinear volatility and option pricing model presented recently by Ivancevic is investigated, which generates a leverage effect, i.e., stock volatility is (negatively) correlated to stock returns, and can be regarded as a…
We study the estimation of leverage effect and volatility of volatility by using high-frequency data with the presence of jumps. We first construct spot volatility estimator by using the empirical characteristic function of the…
In the first quarter of 2006 Chicago Board Options Exchange (CBOE) introduced, as one of the listed products, options on its implied volatility index (VIX). This created the challenge of developing a pricing framework that can…
In this paper we study the short-time behavior of the at-the-money implied volatility for arithmetic Asian options with fixed strike price. The asset price is assumed to follow the Black-Scholes model with a general stochastic volatility…
We use modifications of the Adams method and very fast and accurate sinh-acceleration method of the Fourier inversion (iFT) (S.Boyarchenko and Levendorski\u{i}, IJTAF 2019, v.22) to evaluate prices of vanilla options; for options of…
We consider the problem of valuation of American options written on dividend-paying assets whose price dynamics follows a multidimensional exponential Levy model. We carefully examine the relation between the option prices, related partial…
The discrepancy between realized volatility and the market's view of volatility has been known to predict individual equity options at the monthly horizon. It is not clear how this predictability depends on a forecast's ability to predict…
We consider assets for which price $X_t$ and squared volatility $Y_t$ are jointly driven by Heston joint stochastic differential equations (SDEs). When the parameters of these SDEs are estimated from $N$ sub-sampled data $(X_{nT}, Y_{nT})$,…
We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic…