Andrey Chirikhin’s Post

Credit Valuation Adjustment Whenever we talk about mathematics of Credit Valuation Adjustment, a long formula like the one shown in the cover page of the booklet comes into our mind. It is difficult to understand what each element of this formula intuitively means. I have prepared this booklet to explain CVA to beginners and those seeking clarity on what CVA means and how we compute it. In the coming posts, I will be talking about the practical implementations using Monte Carlo, SGBM, Machine Learning etc. Follow KSHITIJ ANAND for more on Quantitative Finance! #Quant #CVA #Quantij #QFC'24

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#finance #model #artificialintelligence #machinelearning #algorithms 9 AM, 1.7.2024 ✅ A very interesting resource has been made freely available by the @CFA Institute, for all, relating to the building, testing and validating financial models for investment decision making, using a variety of techniques. It's practically a one stop shop for the reviewing various aspects of mathematical model building, not limited to financial or investment modeling alone. ✅ As one who spends substantial time at work building models for process engineering and energy systems analysis, even I find this resource extremely useful. The general good practices of mathematical modeling have been quite well described, so it is useful for all who do various levels of modeling and simulation work. Really hoping to learn something new this week from this document 😍

Following is the Numerical Methods for Finance assignment carried out by Giacomo Pasquetto, Riccardo Tanchis and myself in the past week using the software #R. We were given a dataset of 58 call options and we had to: - Clean it up using log-moneyness, Merton's, monotonicity and convexity constraints. - Construct the volatility smile using both the Newton-Raphson algorithm (constructed manually by us) and the R function "Optim". - Using the volatility nearest at-the-money level, compare the behaviour of the approximated Gamma (using finite difference method) with the exact Gamma for varying values of the underlying asset S0. - Calibrate the volatility for B&S using MSE, and price a Bear Strategy with it. - Using the abovementioned calibrated sigma, compute the Monte Carlo price for a Floating Arithmentic Call Asian Option (payoff in the paper). We used the Euler simulation scheme for a Geometric Brownian Motion to simulate the behavior of the underlying asset S0. - Analyse the behavior of the Monte Carlo price as the number of simulations increases. This work was a success: we wrote about 700 lines of code, which was of great help for our #Rskills. Stay informed, stay ahead.

Continuing the cleanup series, I’m sharing a project that dives into Implied Volatility (IV) calculation using Newton's Method. Implied volatility is a cornerstone of options pricing, capturing the market's expectation of future volatility. This notebook covers: 1️⃣ Newton’s Method Implementation – A root-finding algorithm used to estimate IV based on market prices. 2️⃣ Black-Scholes Pricing Integration – Combining Newton’s Method with the Black-Scholes model for European options. 3️⃣ Visualization of Convergence – Step-by-step visualization of how Newton’s Method iteratively calculates IV. 4️⃣ Practical Example – Calculating IV for a European call option and interpreting the results. What makes this project interesting is the blend of numerical methods with financial modeling, demonstrating how abstract algorithms like Newton's Method solve real-world problems like IV estimation. The notebook also includes dynamic visualizations to better understand the convergence process. If you’re interested in options pricing or numerical methods in finance, this is worth exploring. I’d love to hear your thoughts or feedback! Check it out here: https://lnkd.in/gVgbDkT7

Fitting Hierarchical Generalized Linear Models Use hglm With (In) R Software https://ln.run/hglm Bayesian flexible survival models Use morgana With STATA 18 https://ln.run/morgana

With my friend Sepehr Nour, we are on the #backtest of #financial data using machine learning. We start with #Qlearning using the stochastic Bellman equation through Monte Carlo Learning. We use the Black Scholes #Merton model to account for #Levy flights. These are the test data results for now where the equity curve is nearly linear in 20 days through 30min candles. Start 1900-01-01 00:00:00 End 1900-01-21 20:00:00 Duration 20 days 20:00:00 Exposure Time [%] 89.61039 Equity Final [$] 59313.295839 Equity Peak [$] 59337.856424 Return [%] 493.132958 Buy & Hold Return [%] 36.146801 Return (Ann.) [%] 5348164247550898.0 Volatility (Ann.) [%] 6642803901620927.0 Sharpe Ratio 0.805106 Sortino Ratio inf Calmar Ratio 788969184285577.0 Max. Drawdown [%] -6.778673 Avg. Drawdown [%] -1.220348 Max. Drawdown Duration 1 days 15:00:00 Avg. Drawdown Duration 0 days 03:38:00 # Trades 117 Win Rate [%] 70.08547 Best Trade [%] 9.582252 Worst Trade [%] -4.216105 Avg. Trade [%] 1.578476 Max. Trade Duration 0 days 17:00:00 Avg. Trade Duration 0 days 03:20:00 Profit Factor 6.691525 Expectancy [%] 1.612321 SQN 5.253822 _strategy ActionBasedStrat... _equity_curve ... _trades Size Entry... dtype: object

Machine Learning Model to predict bank deposits ,utilizing the Random Forest Classifier Illustrates the following concepts: IQR - outlier identification and removal Oversampling - Mitigating class imbalances Grid Search - Hyper-tuning Parameters

This is how analytics can aid in strategies in Banking.

Options on quadratic variation: There are several derivatives that have as their underlying the realized variance of an asset, such as volatility and variance swaps and puts and calls on realized variance. A common way of working with these options is to approximate the realized variance over the interval [0,T] by [X,X]_T/T, where [X,X] is the quadratic variation of the log-price X. This approximation is justified because for each fixed T, the realized variance over [0,T] converges to [X,X]_T/T in probability as the number of subdivisions in the calculation of the realized variance tends to infinity (Jacod and Shiryaev (2003), Theorem I.4.47). Keller-Ressel and Muhle-Karbe (2013) present an approximate method to obtain the value of an option on the realized variance through the corresponding option on the quadratic variation. The first of the formulas below, taken from Keller-Ressel and Muhle-Karbe (2013), represents the price of a put option on the quadratic variation when X follows a Lévy process. - E represents the expectation under the pricing measure. - K is the strike. - sigma^2 is the variance of the Brownian motion associated with the Lévy process X. - F is the Lévy measure. In the same paper, an exact method for obtaining the price of options on realized variance using Fourier-Laplace techniques is also presented. Note: In the formula I have corrected what appears to be a typographical error in the original formula of corollary 4.3 (c for sigma squared). References: - Jacod and Shiryaev (2003): "Limit Theorems for Stochastic Processes", Springer. - Keller-Ressel and Muhle-Karbe (2013): "Asymptotic and Exact Pricing of Options on Variance", Finance and Stochastics, 17, 107-133. #finance #mathematics #markets