Spread Options Research Articles

Implied dividend bounds in option prices: anatomy of two markets

Abstract We propose a measure of uncertainty of a dividend paying asset based on the cross-section of bid-ask spreads of options. This is the difference between the cheapest synthetic long position of the asset that it is possible to construct using European options and the most expensive short position that can be constructed at the same time for the same maturity. For index and stock option applications this measure can be compared with other direct measures of uncertainty such as the bid-ask spread of the futures market on the underlying or their dividend. It turns out that for index options the measure is tighter than the bid-ask spread of the futures market for maturities longer than the first two futures contracts. The comparison of the measure for individual stock options with dividend futures gives mixed results. Finally, applying a two-tail distortion (2TD) model we find an asymmetric setting of option ask and bid prices with respect to the reference model. Most of the distortion is loaded on the ask call price and bid put prices. This corresponds to asymmetric uncertainty in dividend yield expectations, which put more weight on low dividends.

Spread Option Pricing Under Finite Liquidity Framework

This work explores a finite liquidity model to price spread options and assess the liquidity impact. We employ Kirk approximation for computing the spread option price and its delta. The latter is needed since the liquidity impact is caused by the delta hedging of a large investor. Our main contribution is a novel methodology to price spread options in this paradigm. Kirk approximation in conjunction with Monte Carlo simulations yields the spread option prices. Moreover, the antithetic and control variates variance reduction techniques improve the performance of our method. Numerical experiments reveal that the finite liquidity causes a liquidity value adjustment in option prices ranging from 0.53% to 2.81%. The effect of correlation on prices is also explored, and as expected the option price increases due to the diversification effect, but the liquidity impact decreases slightly.

Sector Formula for Approximation of Spread Option Value & Greeks and Its Applications

Sector Formula for Approximation of Spread Option Value & Greeks and Its Applications

Pricing vulnerable spread options with liquidity risk under Lévy processes

In this paper, we consider vulnerable spread options with stochastic liquidity risk. Lévy processes are introduced to characterize jumps and we allow the liquidity discount factor to be related to a mean-reversion process. Through bivariate Fourier transforms, we successfully get the approximated pricing formula in the proposed model, and numerical experiments show that the approximated prices are very accurate. We finally focus on the impact of asymmetric jump risk and stochastic liquidity risk on vulnerable spread option prices.

MULTIVARIATE HAWKES-BASED MODELS IN LIMIT ORDER BOOK: EUROPEAN AND SPREAD OPTION PRICING

In this paper, we consider the pricing problem of European options and spread options for the Hawkes-based model in the limit order book (LOB). We introduce a variant of Hawkes process and consider its limit theorems, namely the exponential multivariate general compound Hawkes process (EMGCHP). We also consider a special case of one-dimensional EMGCHP and its limit theorems. Option pricing with one-dimensional EMGCHP in LOB and numerical examples are presented. We also discuss implied volatility and implied order flow. It reveals the relationship between stock volatility and the order flow in the LOB system. In this way, the Hawkes-based model can provide more market forecast information than the classical Black–Scholes model. Margrabe’s spread options valuations with two one-dimensional and one two-dimensional Hawkes-based models for two assets are presented.

Testing the Closed-Form Spread Option Pricing Formula Based on Gauss-Hermite Quadrature for a Jump-Diffusion Model

Testing the Closed-Form Spread Option Pricing Formula Based on Gauss-Hermite Quadrature for a Jump-Diffusion Model

Excess cash and equity option liquidity

AbstractWe examine the relation between excess corporate cash holdings and equity option market liquidity from January 3, 2005 to December 31, 2019. We show that the level of cash reserve in excess of what can be captured by firm characteristics significantly explains stock option liquidity. Trading volume and option open interest increase in companies with a higher magnitude of excess cash, whereas the bid–ask spreads of stock options decline in excess cash. Our findings confirm the theoretical prediction that excess cash improves option market liquidity as it reduces adverse selection problems caused by uncertainty in firm valuations. This relation remains more pronounced with put options, out‐of‐the‐money contracts, and short‐maturity contracts. In addition, excess cash has a stronger impact on option liquidity within firms that have a greater degree of informed trading and during high‐volatility periods in financial markets. Our results show that when uncertainty about firm prospects rises, excess cash becomes more valuable and affects option market liquidity.

Analytic approximations for European-style Asian spread options

<abstract><p>Spread option is a exotic option, which allows investors to simultaneously take positions in two correlated underlying assets and profit from their price difference over some spread. This option provides stable investment opportunities for practitioners in unpredictable and complex financial markets. However, investors of the spread option may face problems caused by manipulating the two underlying assets' prices near the expiry, compared to plain vanilla options. To overcome such disadvantages, we propose Asian-spread options, which are linked to the price difference between two average prices of two underlying assets over the life of the option, and exhibit the original properties of standard spread options. In this paper, using distribution-approximating and moment-matching approaches, lower bounds of prices for the European spread option on the geometric average Asian option and arithmetic average Asian option are obtained in the classical Black-Scholes model. We verified the pricing accuracy of the proposed Asian-spread options by comparing our solutions with those obtained by Monte Carlo simulations. Finally, we analyzed the influence of stock price, maturity date, and some model parameters on option price and delta value through numerical examples. Numerical results showed that the lower bounds had a very high precision.</p></abstract>

Pricing forward-start style exotic options under uncertain stock models with periodic dividends

<p>In this study, we derived pricing formulas for various forward-start style exotic options based on an uncertain stock models with periodic dividends. Specifically, we present valuations for forward-start, Cliquet/Ratchet, and spread options. In addition, we conducted numerical simulations of these formulas and compared them to pricing formulas for the same options based on a dividend-paying stock model driven by standard Brownian motion.</p>

Pricing of Spread Options: A Stochastic Approach

Pricing of Spread Options: A Stochastic Approach

An efficient unified approach for spread option pricing in a copula market model

An efficient unified approach for spread option pricing in a copula market model

PIN RISK IN OPTION SPREAD STRATEGIES

ABSTRACT Of the two ways to form the bull spread and of the two ways to form the bear spread, two of these four ways will result in non-trivial pin risk, which forcibly assigns investors the underlying shares they originally do not intend to buy or sell. Incidentally, both ways that give rise to the pin risk are credit spreads when initiated. Major investment textbooks, that ignore the existence of the pin risk, mislead their readers into believing the deterministic values of the maximum gain, maximum loss, and the breakeven stock price at maturity. The DNE (do not exercise) option available to debit spread investors offers only limited optimal exit strategy. This note attempts to highlight pin risk in option spread strategies and hopes to narrow the gap between theory and practice. Keywords Pin risk, investors, strategy

Valuation of spread options under correlated skew Brownian motions

In this paper, we employ correlated skew Brownian motions to describe the dynamics of the two assets underlying the spread option. In the pricing model, the two underlying assets are exposed to exogenous risks captured by the same Brownian motion, and their endogenous risks are also assumed to be correlated with each other. We obtain an approximate pricing formula of spread options and calibrate model parameters to real data. In addition, we compare the results obtained from the approximate formula with those derived from the exact closed-form formula and from the Monte Carlo method. Finally, we analyze the impact of the skewness parameter on option prices after checking the accuracy of the approximations numerically.

Spread Option Pricing Based on Black-Scholes Model and Monte Carlo Simulation Under the Situation of Russia-Ukraine

In 2022, under the current situation of Russia and Ukraine as well as the outbreak of epidemics, the price of crude oil and gasoline are fluctuating dramatically. On this basis, investors face great uncertainty in the future markets. To find out a way to help investors benefit from the war, we used the current information to estimate future trends. By applying the Monte Carlo model to generate random numbers, Black-Scholes model is applied to price the future option based on the data from Yahoo Finance. In addition, the benchmark simulation is employed to obtain a more accurate option value. Spread option has both strengths and weaknesses. Specifically, it can help investors to earn their profits and minimize the risks, while will fluctuate the price of the option when the two assets are highly correlated thus reducing the value of the option. According to sensitive analysis, the positive relationship is clarified between the option pricing as well as the volatility and time period. These results shed light on the best strategy for the clients to make more profits. It is concluded that customers should hold their stocks for the long term and sell them for a higher profit when the war is over.

A closed-form approximation for pricing spread options on futures under a mean-reverting spot price model with multiscale stochastic volatility

Abstract Commodity spot prices tend to revert to some long-term mean level and most commodity derivatives are based on futures prices, not on spot prices. So, we consider spread options on futures instead of spot or spot index, where the log spot price follows a mean-reverting process. The volatility of the mean-reverting process is driven by two different (fast and slow) scale factors. We use asymptotic analysis to obtain a closed-form approximation of the futures prices and a closed-form formula for the approximate prices of spread options on the futures. The overall improvement of our analytic formula over the classical Kirk–Bjerksund–Sternsland (KBS) formula is discussed via numerical experiments.

A novel stochastic modeling framework for coal production and logistics through options pricing analysis

We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory. The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model. We derive a three-dimensional Fast Fourier Transform (“FFT”) lower bound approximation to value the inherent real optionality and for robustness check, we compare the semi-analytical pricing accuracy with the Monte Carlo simulation. Model parameters are estimated from the historical monthly data, and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross (“CIR”) model.

CMS Spread Options Pricing under the CHH Model

Based on the Chen, Hsieh, and Huang (2017) interest rate model, this research explores the analytical approach for pricing CMS spread options. We first derive a complex joint density for two swap rates composed of sequential forward rates and approximate the joint density by bivariate normals. After applying the methods of Pearson (1995) and Li, Deng, and Zhou (2008), we obtain two analytical pricing models and examine their accuracy using numerical analysis. Finally, we empirically show the predictive power of the implied volatility of CMS options for future economic states.

Research On the Pricing of Oil Spread Option Based on Geometric Brownian Motion

On Monday, 21 April 2020, for the first time ever in its existence, the price of US crude oil declined. This study constructs a spread option using geometric Brownian motion and simulates the prices of WTI oil and heating oil, both from the Chicago Mercantile Exchange (CME) Group, and processes and simulates them on a Microsoft Excel basis. This paper predicts the pricing of spread option by the heating oil price and compared to the Asian and European options. The results obtained showed that the volatility of the heating oil price affects the premium of the spread option. The significance of this paper is for investors to compare different options and find profit opportunities to make investment decisions.

Calendar Spread Options on Energy Commodities

Calendar Spread Options on Energy Commodities

Pricing Vulnerable Spread Options under an Intensity-based Model

Pricing Vulnerable Spread Options under an Intensity-based Model