Academic literature on the topic 'Bates model with lognormal jumps'
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Bates model with lognormal jumps.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Journal articles on the topic "Bates model with lognormal jumps"
1
BROADIE, MARK, and ASHISH JAIN. "THE EFFECT OF JUMPS AND DISCRETE SAMPLING ON VOLATILITY AND VARIANCE SWAPS." International Journal of Theoretical and Applied Finance 11, no. 08 (December 2008): 761–97. http://dx.doi.org/10.1142/s0219024908005032.
Full textAbstract:
We investigate the effect of discrete sampling and asset price jumps on fair variance and volatility swap strikes. Fair discrete volatility strikes and fair discrete variance strikes are derived in different models of the underlying evolution of the asset price: the Black-Scholes model, the Heston stochastic volatility model, the Merton jump-diffusion model and the Bates and Scott stochastic volatility and jump model. We determine fair discrete and continuous variance strikes analytically and fair discrete and continuous volatility strikes using simulation and variance reduction techniques and numerical integration techniques in all models. Numerical results show that the well-known convexity correction formula may not provide a good approximation of fair volatility strikes in models with jumps in the underlying asset. For realistic contract specifications and model parameters, we find that the effect of discrete sampling is typically small while the effect of jumps can be significant.
2
Baek, In Seok, and Byung Jin Kang. "The Dynamic Behavior of Foreign Exchange Rates with Stochastic Volatility and Jump Diffusion Models-Evidences from KRW/USD Spot and Option Markets." Journal of Derivatives and Quantitative Studies 19, no. 1 (February 28, 2011): 1–36. http://dx.doi.org/10.1108/jdqs-01-2011-b0001.
Full textAbstract:
This paper assesses the empirical performances of the continuous-time models, including constant volatility (Black and Scholes, 1973), stochastic volatility (Heston, 1993), and stochastic volatility with jumps (Bates, 1996), in FX spot and option markets. To analyze the spot market, we used the EMM (Efficient Method of Moments) methods with daily KRW/USD spot exchange rates from November 1997 through July 2009. First, the empirical results find that the Bates model highly outperforms the other modelsin explaining the dynamic behavior of KRW/USD spot exchange rates. Second, we also find that the jump components carry out an important role in generating leptokurtic properties of KRW/USD spot exchange rates, on the other hand, stochastic volatilities perform a critical role in generating skewed properties of them. To analyze the option market, we examined the daily cross-sectional prices of the KRW/USD OTC options from January 2006 through March 2010. The empirical results from the option markets confirm that the Bates model clearly outperforms the other modelsin explaining the observed patterns of implied-volatility smile or smirk.
3
Stilger, Przemyslaw S., Ngoc Quynh Anh Nguyen, and Tri Minh Nguyen. "Empirical performance of stochastic volatility option pricing models." International Journal of Financial Engineering 08, no. 01 (January 19, 2021): 2050056. http://dx.doi.org/10.1142/s2424786320500565.
Full textAbstract:
This paper examines the empirical performance of four stochastic volatility option pricing models: Heston, Heston[Formula: see text], Bates and Heston–Hull–White. To compare these models, we use individual stock options data from January 1996 to August 2014. The comparison is made with respect to pricing and hedging performance, implied volatility surface and risk-neutral return distribution characteristics, as well as performance across industries and time. We find that the Heston model outperforms the other models in terms of in-sample pricing, whereas Heston[Formula: see text] model outperforms the other models in terms of out-of-sample hedging. This suggests that taking jumps or stochastic interest rates into account does not improve the model performance after accounting for stochastic volatility. We also find that the model performance deteriorates during the crises as well as when the implied volatility surface is steep in the maturity or strike dimension.
4
Singh, Vipul Kumar. "Pricing competitiveness of jump-diffusion option pricing models: evidence from recent financial upheavals." Studies in Economics and Finance 32, no. 3 (August 3, 2015): 357–78. http://dx.doi.org/10.1108/sef-08-2012-0099.
Full textAbstract:
Purpose – The purpose of this paper is to investigate empirically the forecasting performance of jump-diffusion option pricing models of (Merton and Bates) with the benchmark Black–Scholes (BS) model relative to market, for pricing Nifty index options of India. The specific period chosen for this study canvasses the extreme up and down limits (jumps) of the Indian capital market. In addition, equity markets keep on facing high and low tides of financial flux amid new economic and financial considerations. With this backdrop, the paper focuses on finding an impeccable option-pricing model which can meet the requirements of option traders and practitioners during tumultuous periods in the future. Design/methodology/approach – Envisioning the fact, the all option-pricing models normally does wrong valuation relative to market. For estimating the structural parameters that governs the underlying asset distribution purely from the underlying asset return data, we have used the nonlinear least-square method. As an approach, we analyzed model prices by dividing the option data into 15 moneyness-maturity groups – depending on the time to maturity and strike price. The prices are compared analytically by continuously updating the parameters of two models using cross-sectional option data on daily basis. Estimated parameters then used to figure out the forecasting performance of models with corresponding BS and market – for pricing day-ahead option prices and implied volatility. Findings – The outcomes of the paper reveal that the jump-diffusion models are a better substitute of classical BS, thus improving the pricing bias significantly. But compared to jump-diffusion model of Merton’s, the model of Bates’ can be applied more uniquely to find out the pricing of three popularly traded categories: deep-out-of-the-money, out-of-the-money and at-the-money of Nifty index options. Practical implications – The outcome of this research work reveals that the jumps are important components of pricing dynamics of Nifty index options. Incorporation of jump-diffusion process into option pricing of Nifty index options leads to a higher pricing effectiveness, reduces the pricing bias and gives values closer to the market. As the models have been tested in extreme conditions to determine the dominant effectuality, the outcome of this paper helps traders in keeping the investment protected under normal conditions. Originality/value – The specific period chosen for this study is very unique; it canvasses the extreme up and down limits (jumps) of the Indian capital market and provides the most apt situation for testifying the pricing competitiveness of the models in question. To testify the robustness of models, they have been put into a practical implication of complete cycle of financial frame.
5
LI, T. RAY, and MARIANITO R. RODRIGO. "Alternative results for option pricing and implied volatility in jump-diffusion models using Mellin transforms." European Journal of Applied Mathematics 28, no. 5 (December 6, 2016): 789–826. http://dx.doi.org/10.1017/s0956792516000516.
Full textAbstract:
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.
6
MERINO, R., J. POSPÍŠIL, T. SOBOTKA, and J. VIVES. "DECOMPOSITION FORMULA FOR JUMP DIFFUSION MODELS." International Journal of Theoretical and Applied Finance 21, no. 08 (December 2018): 1850052. http://dx.doi.org/10.1142/s0219024918500528.
Full textAbstract:
In this paper, we derive a generic decomposition of the option pricing formula for models with finite activity jumps in the underlying asset price process (SVJ models). This is an extension of the well-known result by Alòs [(2012) A decomposition formula for option prices in the Heston model and applications to option pricing approximation, Finance and Stochastics 16 (3), 403–422, doi: https://doi.org/10.1007/s00780-012-0177-0 ] for Heston [(1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options, The Review of Financial Studies 6 (2), 327–343, doi: https://doi.org/10.1093/rfs/6.2.327 ] SV model. Moreover, explicit approximation formulas for option prices are introduced for a popular class of SVJ models — models utilizing a variance process postulated by Heston [(1993) A closed-form solution for options with stochastic volatility with applications to bond and currency options, The Review of Financial Studies 6 (2), 327–343, doi: https://doi.org/10.1093/rfs/6.2.327 ]. In particular, we inspect in detail the approximation formula for the Bates [(1996), Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche mark options, The Review of Financial Studies 9 (1), 69–107, doi: https://doi.org/10.1093/rfs/9.1.69 ] model with log-normal jump sizes and we provide a numerical comparison with the industry standard — Fourier transform pricing methodology. For this model, we also reformulate the approximation formula in terms of implied volatilities. The main advantages of the introduced pricing approximations are twofold. Firstly, we are able to significantly improve computation efficiency (while preserving reasonable approximation errors) and secondly, the formula can provide an intuition on the volatility smile behavior under a specific SVJ model.
7
Mijatović, Aleksandar, Martijn R. Pistorius, and Johannes Stolte. "Randomisation and recursion methods for mixed-exponential Lévy models, with financial applications." Journal of Applied Probability 52, no. 04 (December 2015): 1076–96. http://dx.doi.org/10.1017/s0021900200113099.
Full textAbstract:
We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of the first-passage time probability and expected occupation time of sets of a Lévy bridge process that relies in part on a randomisation of the time parameter. We establish this recursion for general Lévy processes and derive its explicit form for mixed-exponential jump-diffusions, a dense subclass (in the sense of weak approximation) of Lévy processes, which includes Brownian motion with drift, Kou's double-exponential model, and hyperexponential jump-diffusion models. We present a highly accurate numerical realisation and derive error estimates. By way of illustration the method is applied to the valuation of range accruals and barrier options under exponential Lévy models and Bates-type stochastic volatility models with exponential jumps. Compared with standard Monte Carlo methods, we find that the method is significantly more efficient.
8
Mijatović, Aleksandar, Martijn R. Pistorius, and Johannes Stolte. "Randomisation and recursion methods for mixed-exponential Lévy models, with financial applications." Journal of Applied Probability 52, no. 4 (December 2015): 1076–96. http://dx.doi.org/10.1239/jap/1450802754.
Full textAbstract:
We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of the first-passage time probability and expected occupation time of sets of a Lévy bridge process that relies in part on a randomisation of the time parameter. We establish this recursion for general Lévy processes and derive its explicit form for mixed-exponential jump-diffusions, a dense subclass (in the sense of weak approximation) of Lévy processes, which includes Brownian motion with drift, Kou's double-exponential model, and hyperexponential jump-diffusion models. We present a highly accurate numerical realisation and derive error estimates. By way of illustration the method is applied to the valuation of range accruals and barrier options under exponential Lévy models and Bates-type stochastic volatility models with exponential jumps. Compared with standard Monte Carlo methods, we find that the method is significantly more efficient.
9
Howitt, G., A. Melatos, and B. Haskell. "Simulating pulsar glitches: an N-body solver for superfluid vortex motion in two dimensions." Monthly Notices of the Royal Astronomical Society 498, no. 1 (August 29, 2020): 320–31. http://dx.doi.org/10.1093/mnras/staa2314.
Full textAbstract:
ABSTRACT A rotating superfluid forms an array of quantized vortex lines that determine its angular velocity. The spasmodic evolution of the array under the influence of deceleration, dissipation, and pinning forces is thought to be responsible for the phenomenon of pulsar glitches, sudden jumps in the spin frequency of rotating neutron stars. We describe and implement an N-body method for simulating the motion of up to 5000 vortices in two dimensions and present the results of numerical experiments validating the method, including stability of a vortex ring and dissipative formation of an Abrikosov array. Vortex avalanches occur routinely in the simulations, when chains of unpinning events are triggered collectively by vortex–vortex repulsion, consistent with previous, smaller scale studies using the Gross–Pitaevskii equation. The probability density functions of the avalanche sizes and waiting times are consistent with both exponential and lognormal distributions. We find weak correlations between glitch sizes and waiting times, consistent with astronomical data and meta-models of pulsar glitch activity as a state-dependent Poisson process or a Brownian stress-accumulation process, and inconsistent with a threshold-triggered stress-release model with a single, global stress reservoir. The spatial distribution of the effective stress within the simulation volume is analysed before and after a glitch.
Dissertations / Theses on the topic "Bates model with lognormal jumps"
1
Krebs, Daniel. "Pricing a basket option when volatility is capped using affinejump-diffusion models." Thesis, KTH, Matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-123395.
Full textAbstract:
This thesis considers the price and characteristics of an exotic option called the Volatility-Cap-Target-Level(VCTL) option. The payoff function is a simple European option style but the underlying value is a dynamic portfolio which is comprised of two components: A risky asset and a non-risky asset. The non-risky asset is a bond and the risky asset can be a fund or an index related to any asset category such as equities, commodities, real estate, etc. The main purpose of using a dynamic portfolio is to keep the realized volatility of the portfolio under control and preferably below a certain maximum level, denoted as the Volatility-Cap-Target-Level (VCTL). This is attained by a variable allocation between the risky asset and the non-risky asset during the maturity of the VCTL-option. The allocation is reviewed and if necessary adjusted every 15th day. Adjustment depends entirely upon the realized historical volatility of the risky asset. Moreover, it is assumed that the risky asset is governed by a certain group of stochastic differential equations called affine jump-diffusion models. All models will be calibrated using out-of-the money European call options based on the Deutsche-Aktien-Index(DAX). The numerical implementation of the portfolio diffusions and the use of Monte Carlo methods will result in different VCTL-option prices. Thus, to price a nonstandard product and to comply with good risk management, it is advocated that the financial institution use several research models such as the SVSJ- and the Seppmodel in addition to the Black-Scholes model. Keywords: Exotic option, basket option, risk management, greeks, affine jumpdiffusions, the Black-Scholes model, the Heston model, Bates model with lognormal jumps, the Bates model with log-asymmetric double exponential jumps, the Stochastic-Volatility-Simultaneous-Jumps(SVSJ)-model, the Sepp-model.
2
Paulin, Carl, and Maja Lindström. "Option pricing models: A comparison between models with constant and stochastic volatilities as well as discontinuity jumps." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-172226.
Full textAbstract:
The purpose of this thesis is to compare option pricing models. We have investigated the constant volatility models Black-Scholes-Merton (BSM) and Merton’s Jump Diffusion (MJD) as well as the stochastic volatility models Heston and Bates. The data used were option prices from Microsoft, Advanced Micro Devices Inc, Walt Disney Company, and the S&P 500 index. The data was then divided into training and testing sets, where the training data was used for parameter calibration for each model, and the testing data was used for testing the model prices against prices observed on the market. Calibration of the parameters for each model were carried out using the nonlinear least-squares method. By using the calibrated parameters the price was calculated using the method of Carr and Madan. Generally it was found that the stochastic volatility models, Heston and Bates, replicated the market option prices better than both the constant volatility models, MJD and BSM for most data sets. The mean average relative percentage error for Heston and Bates was found to be 2.26% and 2.17%, respectively. Merton and BSM had a mean average relative percentage error of 6.90% and 5.45%, respectively. We therefore suggest that a stochastic volatility model is to be preferred over a constant volatility model for pricing options.Syftet med denna tes är att jämföra prissättningsmodeller för optioner. Vi har undersökt de konstanta volatilitetsmodellerna Black-Scholes-Merton (BSM) och Merton’s Jump Diffusion (MJD) samt de stokastiska volatilitetsmodellerna Heston och Bates. Datat vi använt är optionspriser från Microsoft, Advanced Micro Devices Inc, Walt Disney Company och S&P 500 indexet. Datat delades upp i en träningsmängd och en test- mängd. Träningsdatat användes för parameterkalibrering med hänsyn till varje modell. Testdatat användes för att jämföra modellpriser med priser som observerats på mark- naden. Parameterkalibreringen för varje modell utfördes genom att använda den icke- linjära minsta-kvadratmetoden. Med hjälp av de kalibrerade parametrarna kunde priset räknas ut genom att använda Carr och Madan-metoden. Vi kunde se att de stokastiska volatilitetsmodellerna, Heston och Bates, replikerade marknadens optionspriser bättre än båda de konstanta volatilitetsmodellerna, MJD och BSM för de flesta dataseten. Medelvärdet av det relativa medelvärdesfelet i procent för Heston och Bates beräknades till 2.26% respektive 2.17%. För Merton och BSM beräknades medelvärdet av det relativa medelvärdesfelet i procent till 6.90% respektive 5.45%. Vi anser därför att en stokastisk volatilitetsmodell är att föredra framför en konstant volatilitetsmodell för att prissätta optioner.
Book chapters on the topic "Bates model with lognormal jumps"
1
"The Fundamental Cox, Ingersoll, and Ross Model with Exponential and Lognormal Jumps." In Dynamic Term Structure Modeling, 237–304. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2015. http://dx.doi.org/10.1002/9781119201571.ch6.
Full text