Lookback Call Options with Stochastic Volatility

In this tutorial we are pricing a discretely monitored lookback call option with stochastic volatility. The option payoffs are dependent on the extreme values, maximum or minimum, of the underlying asset prices over a certain time period (lookback period). There are two standard lookback options: fixed strike and floating strike. Fixed strike discrete lookback option options pay the difference (if positive) between the max or min of a set of observations, over a lookback period of the asset price and the strike price at the maturity date.
There is no analytical solution for the price of European fixed strike lookback call options with discrete fixings and stochastic volatility under Heston model. However there is a simple analytical formula for the price of a continuously monitored (fixing) fixed strike lookback call with constant volatility.
We will use a combination of Monte Carlo Variance Reduction techniques such as antithetic and control variate methods to reduce the standard error of our simulation. We use the analytical solution for a continuously monitored fixed strike lookback call option to calculate control variates based on delta, gamma and vega sensitivities.
★ ★ Code Available on GitHub ★ ★
GitHub: github.com/TheQuantPy
Specific Tutorial Link: github.com/TheQuantPy/youtube...
★ ★ QuantPy GitHub ★ ★
Collection of resources used on QuantPy UA-cam channel. github.com/thequantpy
★ ★ Discord Community ★ ★
Join a small niche community of like-minded quants on discord. / discord
★ ★ Support our Patreon Community ★ ★
Get access to Jupyter Notebooks that can run in the browser without downloading python.
/ quantpy
★ ★ ThetaData API ★ ★
ThetaData's API provides both realtime and historical options data for end-of-day, and intraday trades and quotes. Use coupon 'QPY1' to receive 20% off on your first month.
www.thetadata.net/
★ ★ Online Quant Tutorials ★ ★
WEBSITE: quantpy.com.au
★ ★ Contact Us ★ ★
EMAIL: [e-mail]
Disclaimer: All ideas, opinions, recommendations and/or forecasts, expressed or implied in this content, are for informational and educational purposes only and should not be construed as financial product advice or an inducement or instruction to invest, trade, and/or speculate in the markets. Any action or refraining from action; investments, trades, and/or speculations made in light of the ideas, opinions, and/or forecasts, expressed or implied in this content, are committed at your own risk an consequence, financial or otherwise. As an affiliate of ThetaData, QuantPy Pty Ltd is compensated for any purchases made through the link provided in this description.

[@qiguosun129]

This lecture is hard but intuitive.

[@ahsamv1992]

Perfect timing I had and assignment to price look back option and I was lost a bit , but this video helped thanks 🙏🏼

[@eygs493]

how?

[@diego-castro]

Hello friend, I really admire your channel and I'm thinking of doing this, see if it makes sense what I want to do:
1) An algorithm that could calculate possible ranges of values for a given asset. For example a MonteCarlo and with the odds.
2) In this same prediction, see possible volatilities scenarios, using the ARCH and GARCH models for each price sigma in item 1;
3) And finally, calculate the values of certain asset options for the price and vol scenarios predicted in the previous scenarios.

[@jacky305]

Hello, what's the difference among brownian motion , Brownian bridge and geometry Brownian motion?thx for ur answer.

[@rytospar1731]

Hello, I noticed that the Monte Carlo price was much lower (16.28) than the close formula (17.72). Is this expected? Is there a way to make them closer ? Thank you !

[@PABLO-oq1kt]

Don't understand the meme on the thumbnail picture.