Implied Volatility Estimation Research Articles

The stock implied volatility and the implied dividend volatility

This study compares the information on the implied volatility surface of a stock-index with the corresponding information on the implied volatility surface of the index dividend futures. We outline an optimisation technique for comparing implied volatility estimates based on the Black-Scholes model, Black model and a model-free approach, for stock-index versus dividend-index futures. The implied volatility term-structure of stock-index consistently exceeds that of the dividend index futures thereby confirming the equity volatility puzzle under novel financial data and instruments. However, the magnitude of excess implied volatility reduces as the time-to-maturity increases, suggesting that discrepancies between the two are influenced by investment horizon, and the type of option, call or put. We also show the existence of a profitable trading rule that outperforms a benchmark buy-and-hold strategy. The GDP, dollar euro exchange rate and inflation are strong determinants of the implied volatility difference.

Financial volatility modeling with option-implied information and important macro-factors

The research debate on the informational content embedded in option prices mostly approves the incremental predictive power of implied volatility estimates for financial volatility forecasting beyond that contained in GARCH and realized variance models. Contributing to this ongoing debate, we introduce the novel AIM-HEAVY model, a tetravariate system with asymmetries, option-implied volatility, and economic uncertainty variables beyond daily and intra-daily dispersion measures included in the benchmark HEAVY specification. We associate financial with macroeconomic uncertainties to explore the macro-financial linkages in the high-frequency domain. In this vein, we further focus on economic factors that exacerbate stock market volatility and represent major threats to financial stability. Hence, our findings are directly connected to the current world-wide Coronavirus outbreak. Financial volatilities are already close to their crisis-peaks amid the generalized fear about controversial economic policies to support societies and the financial system, especially in the case of the heavily criticized UK authorities’ delayed and limited response.

Turbocharging Monte Carlo pricing for the rough Bergomi model

The rough Bergomi model, introduced by Bayer et al. [Quant. Finance, 2016, 16(6), 887–904], is one of the recent rough volatility models that are consistent with the stylised fact of implied volatility surfaces being essentially time-invariant, and are able to capture the term structure of skew observed in equity markets. In the absence of analytical European option pricing methods for the model, we focus on reducing the runtime-adjusted variance of Monte Carlo implied volatilities, thereby contributing to the model’s calibration by simulation. We employ a novel composition of variance reduction methods, immediately applicable to any conditionally log-normal stochastic volatility model. Assuming one targets implied volatility estimates with a given degree of confidence, thus calibration RMSE, the results we demonstrate equate to significant runtime reductions—roughly 20 times on average, across different correlation regimes.

A Joint Analysis of the KOSPI 200 Option and ODAX Option Markets Dynamics

As a function of strike and time to maturity the implied volatility estimation is a challenging task in financial econometrics. Dynamic Semiparametric Factor Models (DSFM) are a model class that allows for the estimation of the implied volatility surface (IVS) in a dynamic context, employing semiparametric factor functions and time-varying loadings. Because financial asset volatilities move over time, across assets and over markets, this paper analyses volatility interaction between German and Korean stock markets. As proxy for the volatility, factor loadings series derived from a DSFM application on option prices are employed. We examine volatility transmission between the markets under the vector autoregressive (VAR) model framework. Our results show that a shock in the volatility of one market may not translate directly into greater uncertainty in another market and it is unlikely that portfolio investors can benefit from diversification among these markets due to cointegration.

Alternative results for option pricing and implied volatility in jump-diffusion models using Mellin transforms

In this article, we use Mellin transforms to derive alternative results for option pricing and implied volatility estimation when the underlying asset price is governed by jump-diffusion dynamics. The current well known results are restrictive since the jump is assumed to follow a predetermined distribution (e.g., lognormal or double exponential). However, the results we present are general since we do not specify a particular jump-diffusion model within the derivations. In particular, we construct and derive an exact solution to the option pricing problem in a general jump-diffusion framework via Mellin transforms. This approach of Mellin transforms is further extended to derive a Dupire-like partial integro-differential equation, which ultimately yields an implied volatility estimator for assets subjected to instantaneous jumps in the price. Numerical simulations are provided to show the accuracy of the estimator.

Crop Insurance Decisions for 2016

The Risk Management Agency (RMA) has now concluded its price discovery period used to determined final prices and volatility factors for federally sponsored corn and soybean crop insurance products for 2016. For the majority of the Cornbelt, the approved Projected Price (PP) for corn is expected to be $3.86 and the volatility factor is .18. For soybeans, the Projected Price is expected to be $8.85 with a volatility factor of .12. For comparison, the 2015 prices and (volatility factors) were $4.15 (.21) and $9.73 (.16) for corn and soybeans respectively. The Projected Prices are used to determine a guarantee revenue based on futures prices, and do not reflect local basis. The Projected Price for corn is determined by averaging the closing December futures price during the trading days of February, and for soybeans by averaging the November Futures closing prices during February. The volatility factors are determined by an average of the most recent five trading days' implied volatility estimates, scaled for the interval of time from now until the middle of October -the month during which average prices are used to determine Harvest Prices. For both corn and soybeans, the projected prices are lower than in 2015 which in turn were lower than 2014 and so forth, resulting in the lowest average guarantees for the past 6 years for corn and for 4 years for soybeans. The volatility factor summarizes the market’s estimates of the likelihood for price movements of various magnitudes, and has corresponding impacts on premiums paid for Revenue and Harvest Price related products. The relatively low volatilities will result in lower premiums in 2016, all else equal.

The Buffett critique: volatility and long-dated options

In his 2008 letter to shareholders, Warren Buffett, Chairman and CEO of Berkshire Hathaway, criticizes the ability of the Black-Scholes model to accurately price long-dated options. Buffet discusses how the model leads to over-pricing of put options with long maturities using examples of Berkshire’s investments in derivatives contracts. We confirm that traditional implied volatility estimates do indeed overstate long-term volatility. As an alternative, we propose a maturity-matching technique for estimating long-term volatility using historical holding period returns. We focus on three large asset classes, large cap stocks, long-term bonds, and treasury bills, to demonstrate how volatility evolves over different holding periods. We apply this rolling-period simulation method to estimate volatility for annual maturities ranging from 1 to 30-years within the Black-Scholes model. This method generates superior long-dated option values, and effectively answers Buffett’s critique. This is of particular importance for firms with significant investment holdings, as the issuance and valuation of these derivatives can have a substantial effect on firm capital.

Evaluating Crop Insurance Options for 2014

The Risk Management Agency (RMA) has now concluded its price discovery period used to determined final prices and volatility factors for federally sponsored corn and soybean crop insurance products for 2014. For the majority of the cornbelt, the approved Projected Price (PP) for corn is $4.62 and the volatility factor is .19. For soybeans, the projected price is $11.36 with a volatility factor of .13. For comparison, the 2013 prices (volatility factors) were $5.65 (.20) and $12.87 (.17) for corn and soybeans respectively. The Projected Prices are used to determine the guarantee revenue indexes based on futures prices, and do not reflect local basis. The Projected Price for corn is determined by averaging the closing December futures price during the trading days of February, and for soybeans by averaging the November Futures closing prices during February. The volatility factors are determined by an average of the most recent five trading days' implied volatility estimates, scaled for the interval of time from now until the middle of October -the month during which average prices are used to determine Harvest Prices. For both corn and soybeans, the volatility factors have trended downward, and relative to popularly interpreted measures of volatility are considered very low for soybeans in particular. The volatility factor summarizes the market’s estimates of the likelihood for price movements of various magnitudes, and has corresponding impacts on premiums paid for Revenue and Harvest Price related products. In 2014, the Projected Prices for soybeans are close to current futures market prices, while corn traded around $.14 higher than the projected price on the first sales date for crop insurance. When actual futures prices are below the projected price, there is a somewhat increased likelihood for experiencing an insured revenue shortfall, and when actual futures prices are higher than the projected price, there is an increased likelihood that products with the harvest price option embedded will have an increase in guarantee value. Beginning with the 2014 crop, the projected prices and volatilities, where relevant, are now common over both farm-level and area-revenue and area-yield policies.

The Realised–Implied Volatility Relationship: Recent Empirical Evidence from FTSE‐100 Stocks

ABSTRACTThis paper examines the long‐run relationship between implied and realised volatility for a sample of 16 FTSE‐100 stocks. We find strong evidence of long‐memory, fractional integration in equity volatility and show that this long‐memory characteristic is not an outcome of structural breaks experienced during the sample period. Fractional cointegration between the implied and realised volatility is shown using recently developed rank cointegration tests by Robinson and Yajima (2002). The predictive ability of individual equity options is also examined and composite implied volatility estimates are shown to contain information on future idiosyncratic or stock‐specific risk that is not captured using popular statistical approaches. Implied volatilities on individual UK equities are thus closely related to realised volatility and are an effective forecasting method particularly over medium forecasting horizons. Copyright © 2011 John Wiley & Sons, Ltd.

Implied Volatility Surface Estimation Using Transductive Gaussian Fields Regression

Implied volatility estimation is one of the fundamental tasks for asset pricing and risk management. In this paper, we investigate the applicability of semi-supervised regression techniques to estimate an implied volatility surface from the real market option data. Specifically, we employ a transductive Gaussian field regression method since it is able to predict a distribution of the implied volatilities for unlabelled data using only partially labeled data. We've conducted simulation on S&P 500 index data before and after the global financial crisis with discussions of the observed empirical properties of the method.

The informational quality of implied volatility and the volatility risk premium

This article examines the informational quality of implied volatility in forecasting future realized volatility using daily S&P 500 and S&P 100 index option prices from 2000 to 2006. In contrast to many previous studies, we find that implied volatility is an unbiased and efficient estimator of future realized volatility. Unlike implied volatility estimates; both historical and conditional volatility estimates using GARCH and EGARCH models possess limited explanatory power. A delta-hedged trading strategy with long positions in calls, however, generates significantly negative profits that imply a misspecification of constant volatility models. These results suggest that implied volatility estimates from constant volatility models contain valuable information, even though the model might be misspecified.

A Joint Analysis of the KOSPI 200 Option and ODAX Option Markets Dynamics

As a function of strike and time to maturity the implied volatility estimation is a challenging task in nancial econometrics. Dynamic Semiparametric Factor Models (DSFM) are a model class that allows for the estimation of the implied volatility surface (IVS) in a dynamic context, employing semiparametric factor functions and time-varying loadings. Because nancial asset volatilities move over time, across assets and over markets, this paper analyses volatility interaction between German and Korean stock markets. As proxy for the volatility, factor loadings series derived from a DSFM application on option prices are employed. We examine volatility transmission between the markets under the vector autoregressive (VAR) model framework. Our results show that a shock in the volatility of one market may not translate directly into greater uncertainty in another market and it is unlikely that portfolio investors can benet from diversication among these markets due to cointegration.

A refined approach to estimating the implied volatility

In this paper we used a refined approach to estimating the implied volatility from options price in the classic framework developed by Black and Scholes (1973) and Merton (1973). Our study extend the formula previously developed by Corrado and Miller (1996) which works well for the Index options with the present value of strike price being close to the index price. Our refined approach provides more accurate implied volatility estimation over a wider range of moneyness.

Convergence rates of symplectic Pontryagin approximations in optimal control theory

Many inverse problems for differential equations can be formulated as optimal control problems. It is well known that inverse problems often need to be regularized to obtain good ap- proximations. This work presents a systematic method to regularize and to establish error estimates for approximations to some control problems in high dimension, based on symplectic approximation of the Hamiltonian system for the control problem. In particular the work derives error estimates and constructs regularizations for numerical approximations to optimally controlled ordinary differ- ential equations in R d , with non smooth control. Though optimal controls in general become non smooth, viscosity solutions to the corresponding Hamilton-Jacobi-Bellman equation provide good the- oretical foundation, but poor computational efficiency in high dimensions. The computational method here uses the adjoint variable and works efficiently also for high dimensional problems with d � 1. Controls can be discontinuous due to a lack of regularity in the Hamiltonian or due to colliding back- ward paths, i.e. shocks. The error analysis, for both these cases, is based on consistency with the Hamilton-Jacobi-Bellman equation, in the viscosity solution sense, and a discrete Pontryagin principle: the bi-characteristic Hamiltonian ODE system is solved with a C 2 approximate Hamiltonian. The error analysis leads to estimates useful also in high dimensions since the bounds depend on the Lipschitz norms of the Hamiltonian and the gradient of the value function but not on d explicitly. Applications to inverse implied volatility estimation, in mathematical finance, and to a topology optimization problem are presented. An advantage with the Pontryagin based method is that the Newton method can be applied to efficiently solve the discrete nonlinear Hamiltonian system, with a sparse Jacobian that can be calculated explicitly.

Errors in Implied Volatility Estimation

Estimating implied volatility by inverting the Black-Scholes formula is subject to considerable error when option characteristics are observed with plausible errors. Especially for options away from the money, large changes in volatility produce small changes in option prices. Conversely, small errors in option prices and other option characteristics produce large errors in implied volatilities. In the presence of small measurement errors, unobserved truncation of option prices that violate lower bounds for absence of arbitrage can also lead to systematic volatility smiles. The paper proposes feasible GLS estimators that reduce the noise and bias in implied volatility estimates.

A neural network versus Black–Scholes: a comparison of pricing and hedging performances

AbstractAn Erratum has been published for this article in Journal of Forecasting 22(6‐7) 2003, 551 The Black–Scholes formula is a well‐known model for pricing and hedging derivative securities. It relies, however, on several highly questionable assumptions. This paper examines whether a neural network (MLP) can be used to find a call option pricing formula better corresponding to market prices and the properties of the underlying asset than the Black–Scholes formula. The neural network method is applied to the out‐of‐sample pricing and delta‐hedging of daily Swedish stock index call options from 1997 to 1999. The relevance of a hedge‐analysis is stressed further in this paper. As benchmarks, the Black–Scholes model with historical and implied volatility estimates are used. Comparisons reveal that the neural network models outperform the benchmarks both in pricing and hedging performances. A moving block bootstrap is used to test the statistical significance of the results. Although the neural networks are superior, the results are sometimes insignificant at the 5% level. Copyright © 2003 John Wiley & Sons, Ltd.

Implied Volatility in the U.K. Commercial Property Market: Empirical Evidence Based on Transaction Data

The primary aim of this research is to compute implied volatility based on a stochastic contingent claim valuation model proposed by Dixit and Pindyck (1994). Over the sample period of 1984 to 1997, and with approximately 20,000 commercial property transactions in the United Kingdom, we find that implied volatility of rental returns is in the region of 24.83 percent. Over the same sample period, the historical and conditional standard deviations of the log returns of transaction-based rental series is estimated to be 15.60 percent and 35.64 percent, respectively. The tests of information content of these risk measures show that there is strong orthogonality in the information impounded in implied volatility estimates compared to that contained in historical standard deviations.

The Pricing of SPI Futures Options with Daily Futures Style Margin Payments

Empirical evidence on the pricing behaviour of options on index futures contracts traded on USA and UK futures markets reveals that pricing errors and implied volatility estimates differ systematically across exercise price and time to maturity. The introduction on 17 June 1985 of options on share price index futures contracts on the Sydney Futures Exchange, presents the opportunity to examine the pricing of pure futures options, that is, options with daily futures style margin payments. This paper examines the pricing of SPI futures options The results reveal that the pricing of SPI futures options is not well described by a pure futures option pricing model derived under the assumptions of frictionless markets and non-stochastic interest rates. The model underprices both call and put options. Further, implied volatility increases as the option becomes more in/out-of-the-money.

FORECASTING VOLATILITY FOR PORTFOLIO SELECTION

The volatility of an asset is a primary input to the portfolio selection problem. Information about volatility is available from two sources, namely the share market and the option market. This paper examines the forecasting performance, over a three month investment horizon, of time series forecasts (from the share market) and option based implied volatilities. Three time series models, including GARCH, are used and twenty four implied volatility estimation models are employed. Using a data set of twelve UK companies, it is demonstrated that implied volatilities produce better individual forecasts than time series. However, more remarkably, forecasts combining implied volatilies and time series estimates significantly outperform both component forecasts.

Prices and hedge ratios of average exchange rate options

In this paper an analytic approximation for the value of average (or Asian) exchange rate options is derived. The approximation formula is of the Black-Scholes type in which the striking price has been adjusted. It is found that especially in terms of implied volatility estimation errors, the approximation is very accurate. Analytic expressions for several hedge parameters are also derived.