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Yes exactly. By call-put parity you have, for a given strike K and maturity T, with sigma the Black-Scholes (BS) implied volatility from the call price: put_price = callBS(sigma) + K.exp(-r.T) - S = putBS(sigma) So the BS implied volatility of the put is equal to the BS implied volatility of the call.

SABR would be more applicable to interpolate / extrapolate time slice volatility curves or for the pricing of path-independent options as there is no parameter to control the term structure of volatility in this model. Heston is more suitable to price path-dependent exotic options, to model the whole volatility surface when you need to price options with different strikes and different maturities as it uses additional parameters to model the term structure of volatility with a mean-reverting Cox-Ingersoll Ross process for the instantaneous volatility. If you are interested to go further, here is the link to our course on the topic: quant-next.com/product/options-pricing-and-risk-management-part-3/

Adding these new parameters allows to build different shapes of volatility surface, while it is flat under the Black-Scholes model. The different parameters can be calibrated to fit as best as possible the observed volatility surface. Stochastic volatility models such as SABR or Heston can be used for interpolation / extrapolation of the volatility surface or to price exotic products. The prime objective of such model is not to predict the future level of volatility or underlying asset price but to price and risk manage options. If you are interested, please have a look at our course: quant-next.com/product/options-pricing-and-risk-management-part-3/ Best regards, Quant Next quant-next.com/

@@quantnext4773 I truly appreciate the huge effort made by this model to build different shapes of volatility surface and extrapolate the same. However, my concern is what will be the accuracy when 6 different variables are used and many of the variables are stochastic

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Hello, Thanks for your interest in our videos. If you are interested in applications of stochastic calculus in finance, you might be interested in our course on Options, Pricing and Risk Management Part I: quant-next.com/product/option-pricing-risk-management-part1/ Best regards, Quant Next quant-next.com/

Hello Surya, Thanks for your interest in Quant Next. Through the course, you will see with Python code: - how to price vanilla options with the Heston model using the semi-analytic formula and compare it with Monte Carlo simulations - how the different Heston parameters impact the shape of the volatility surface - how to calibrate the parameters to market prices - how to estimate the risk neutral density function from the characteristic function with Fast Fourier transform - how to price a path dependent exotic options by Monte Carlo simulations and path independent ones by numerical integration Best regards, Quant Next

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Yes of course, thanks for spotting it! The extract has been deleted.

A company is more leveraged when its stocks are going down. The debt-to-equity ratio, calculated by dividing a company's total liabilities by its shareholder equity will typically increase when stocks are lower all other things equal.

Thanks for the feedback. We used here implied volatility for call prices. This being said, the volatility implied by a put price will be very similar than the volatility implied by a call price with same expiry and strike price.

Hello, If you are interested to go more in depth, we propose one full course dedicated to the Heston model including applications and tutorials in Python: quant-next.com/product/the-heston-model-for-option-pricing/

i suspect the two terms come from product rule of the derivative, but does it mean the first term should not have the probability density function, but the derivative of it?

Hello, this is the Leibniz integral rule (cf en.wikipedia.org/wiki/Leibniz_integral_rule)

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Thanks a lot for the support! If you are interested in finite difference methods for option pricing, please have a look on our website, there is a course available on this topic: quant-next.com/product/finite-difference-methods-for-option-pricing/

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Bonjour, Yes i am :), but all videos and courses are in English. Best regards

Thank you very much for your support! I obtained the density of the stock price implied by the Heston model from European call options priced with the Heston model (with "real" probability parameters) using the Breeden-Litzenberg formula which derives the underlying return distribution from option prices. Another way to obtain the density of the stock price implied by the Heston model could be by using its characteristic function (we don't know the density but we know the characteristic function with the Heston model) and we recover the density function the Fourier inversion theorem. I will talk about it in future videos.

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Dear Rakesh, thanks for your interest in quant finance. This videos will be indeed part of a full course on Options, Pricing and Risk Management (coming soon!). If you are interested in this course, please leave us your email and we’ll get back to you as soon as it is ready : contact@quant-next.com

Hi, We provide videos and courses on quantitative finance. Yoy may need additional training on probability and stochastic processes. We already provide some introduction videos on stochastic calculus: th-cam.com/play/PLDRKecZj6C2ye5ou9OmhHs2OBpjEhfpoV.html but you may be interested in additional ones on probability. Please contact us: contact@quant-next.com

Sure, please contact us: contact@quant-next.com

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