scholarly journals Anomalous Diffusions in Option Prices: Connecting Trade Duration and the Volatility Term Structure

2019 ◽  
Author(s):  
Antoine Jacquier ◽  
Lorenzo Torricelli
Keyword(s):  
Term Structure ◽  
Option Prices

CALIBRATION OF STOCHASTIC VOLATILITY MODELS VIA SECOND-ORDER APPROXIMATION: THE HESTON CASE

2015 ◽  
Vol 18 (06) ◽  
pp. 1550036 ◽  
Author(s):  
ELISA ALÒS ◽  
RAFAEL DE SANTIAGO ◽  
JOSEP VIVES
Keyword(s):  
Term Structure ◽  
Implied Volatility ◽  
Order Approximation ◽  
Calibration Procedure ◽  
Computational Effort ◽  
Heston Model ◽  
Option Prices ◽  
Volatility Models ◽  
Short And Long Term ◽  
Long Term Behavior

In this paper, we present a new, simple and efficient calibration procedure that uses both the short and long-term behavior of the Heston model in a coherent fashion. Using a suitable Hull and White-type formula, we develop a methodology to obtain an approximation to the implied volatility. Using this approximation, we calibrate the full set of parameters of the Heston model. One of the reasons that makes our calibration for short times to maturity so accurate is that we take into account the term structure for large times to maturity: We may thus say that calibration is not "memoryless," in the sense that the option's behavior far away from maturity does influence calibration when the option gets close to expiration. Our results provide a way to perform a quick calibration of a closed-form approximation to vanilla option prices, which may then be used to price exotic derivatives. The methodology is simple, accurate, fast and it requires a minimal computational effort.

VIX VERSUS VXX: A JOINT ANALYTICAL FRAMEWORK

2020 ◽  
Vol 23 (05) ◽  
pp. 2050033 ◽  
Author(s):  
MARTINO GRASSELLI ◽  
LAKSHITHE WAGALATH
Keyword(s):  
Term Structure ◽  
Real Data ◽  
Analytical Framework ◽  
Option Prices ◽  
Options Market ◽  
Vix Futures ◽  
Consistent Manner ◽  
Systematic Behavior ◽  
Exchange Traded Notes ◽  
Reference Index

We propose a framework for modeling in a consistent manner the VIX index and the VXX, an exchange-traded note written on the VIX. Our study enables to link the properties of VXX to those of the VIX in a tractable way. In particular, we quantify the systematic loss observed empirically for VXX when the VIX futures term-structure is in contango and we derive option prices, implied volatilities and skews of VXX from those of VIX in infinitesimal developments. We also perform a calibration on real data which highlights the flexibility of our model in fitting the futures and the vanilla options market of VIX and VXX. Our framework can be used to model other exchange-traded notes on the VIX as well as any market where exchange-traded notes have been introduced on a reference index, hence providing tools to better anticipate and quantify systematic behavior of an exchange-traded note with respect to the underlying index.

scholarly journals Approximation Formula for Option Prices under Rough Heston Model and Short-Time Implied Volatility Behavior

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1878
Author(s):  
Siow Woon Jeng ◽  
Adem Kilicman
Keyword(s):  
Term Structure ◽  
Taylor Expansion ◽  
Implied Volatility ◽  
Order Approximation ◽  
Heston Model ◽  
Approximation Formula ◽  
Option Prices ◽  
Second Order Approximation ◽  
Time Term ◽  
Short Time

Rough Heston model possesses some stylized facts that can be used to describe the stock market, i.e., markets are highly endogenous, no statistical arbitrage mechanism, liquidity asymmetry for buy and sell order, and the presence of metaorders. This paper presents an efficient alternative to compute option prices under the rough Heston model. Through the decomposition formula of the option price under the rough Heston model, we manage to obtain an approximation formula for option prices that is simpler to compute and requires less computational effort than the Fourier inversion method. In addition, we establish finite error bounds of approximation formula of option prices under the rough Heston model for 0.1≤H<0.5 under a simple assumption. Then, the second part of the work focuses on the short-time implied volatility behavior where we use a second-order approximation on the implied volatility to match the terms of Taylor expansion of call option prices. One of the key results that we manage to obtain is that the second-order approximation for implied volatility (derived by matching coefficients of the Taylor expansion) possesses explosive behavior for the short-time term structure of at-the-money implied volatility skew, which is also present in the short-time option prices under rough Heston dynamics. Numerical experiments were conducted to verify the effectiveness of the approximation formula of option prices and the formulas for the short-time term structure of at-the-money implied volatility skew.

Term structure movements implicit in Asian option prices

2012 ◽  
Vol 12 (1) ◽  
pp. 119-134 ◽  
Author(s):  
Caio Almeida ◽  
José Vicente
Keyword(s):  
Term Structure ◽  
Asian Option ◽  
Option Prices

scholarly journals GARCH Generated Volatility Indices of Bitcoin and CRIX

2020 ◽  
Vol 13 (6) ◽  
pp. 121 ◽  
Author(s):  
Pierre J. Venter ◽  
Eben Maré
Keyword(s):  
Option Pricing ◽  
Term Structure ◽  
Implied Volatility ◽  
Conditional Heteroskedasticity ◽  
Option Prices ◽  
Pricing Model ◽  
European Option ◽  
Short Term ◽  
Market Prices ◽  
Option Pricing Model

In this paper, the pricing performance of the generalised autoregressive conditional heteroskedasticity (GARCH) option pricing model is tested when applied to Bitcoin (BTCUSD). In addition, implied volatility indices (30, 60-and 90-days) of BTCUSD and the Cyptocurrency Index (CRIX) are generated by making use of the symmetric GARCH option pricing model. The results indicate that the GARCH option pricing model produces accurate European option prices when compared to market prices and that the BTCUSD and CRIX implied volatility indices are similar when compared, this is consistent with expectations because BTCUSD is highly weighted when calculating the CRIX. Furthermore, the term structure of volatility indices indicate that short-term volatility (30 days) is generally lower when compared to longer maturities. Furthermore, short-term volatility tends to increase to higher levels when compared to 60 and 90 day volatility when large jumps occur in the underlying asset.

scholarly journals The Equity Curve and Its Relation to Future Stock Returns

2020 ◽  
Vol 13 (2) ◽  
pp. 19
Author(s):  
Olaf Stotz
Keyword(s):  
Stock Returns ◽  
Term Structure ◽  
Investment Strategy ◽  
Absolute Difference ◽  
Option Prices ◽  
Positive Slope ◽  
Short Term ◽  
Theoretical Predictions ◽  
Expected Stock Returns

Using option prices, a new method for estimating the term structure of expected stock returns (equity curve) is proposed. We analyse how the equity curve relates to future stock returns and obtain three main results. First, a higher level of the equity curve is associated with higher future stock returns. Second, a positive slope is followed by future realized returns which are lower in the short term (1 month) than in the long term (1 quarter or 1 year). Third, a steeper slope (either positive or negative) is associated with a larger absolute difference between short-term and long-term returns. Therefore, the equity curve is consistent with theoretical predictions. We also analyse an investment strategy that uses the slope of the equity curve to determine the allocation to stocks. This strategy earns an outperformance of up to 200 basis points per annum.

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