Questions tagged [simulations]
Reproduction of the characteristics or the outcome of a phenomenon or process using math or programming. Here limited to events related with quantitative finance as defined in the help center.
275 questions
0 votes
0 answers
73 views
Simulating stock returns GARCH-copula approach
I am currently in need of simulating stock returns from 2025 until 2100 for scenario analysis purpose. I used a GARCH-copula approach : mean = ARX for GARCH, student t residuals and student t copula. ...
- 31
2 votes
1 answer
236 views
Option Hedging: simulation of cumulative hedged paths and discounting
I'm trying to replicate the Figure 5.1 at pag 96 of Volatility Smile by Derman & Miller where they show that the (cumulative discounted) P&Ls of a hedged portfolio, where the call is evaluated ...
- 455
1 vote
2 answers
365 views
Girsanov Theorem: how to implement it with code?
I'm trying to visualize the path transformations coming from the application of the Girsanov Theorem in a Monte Carlo Simulation. Below the (Python) code where I'm trying to "adjust" the ...
- 455
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132 views
Generation of two correlated Brownian Motions using two different approaches in numpy Python
Consider two correlated Brownian Motions $W_{1,t}$ and $W_{2,t}$ for which it holds: $$dW_{1,t}\sim N(0, \sqrt{dt})$$ $$dW_{2,t}\sim N(0, \sqrt{dt})$$ $$Cov(dW_{1,t},dW_{2,t}) = E[dW_{1,t}dW_{2,t}] = \...
- 157
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68 views
Bachelier delta numerical implementation inconsistency
I'm working with Bachelier model to hedge futures exchange options, based on the formulas here, adapted to derivation to sympy. I have seen 2 very different ...
2 votes
0 answers
76 views
What model(s) can be used to simulate the joint dynamics of the 2y forward curve and implied volatility surface?
I am trying to train a reinforcement learning model for dynamic hedging like Cao et al. 2023. Their model uses SABR to generate joint dynamics of implied volatility and underlying equity asset prices. ...
- 21
3 votes
1 answer
465 views
Delta of European Call using Malliavin Calculus
I am trying to implement the calculation of the Delta under the Heston model using Malliavin Calculus in python. According to "Malliavin Calculus in Finance" by Álos, the Malliavin delta is ...
- 175
2 votes
0 answers
76 views
Is Copula Modeling Suitable for Accounting for Temporal Dynamics in Olive Plantation Data?
I am working on a project analyzing olive plantation data, where I aim to simulate the relationship between investment costs (Costs), revenues (...
- 211
1 vote
0 answers
117 views
Simulating realized variance
I have a question regarding possible ways to simulate realized variance (the sum of squared intraday returns) for testing different realized variance forecasting models. I'm aware of several ...
1 vote
0 answers
169 views
Ornstein-Uhlnbeck Process with Jumps
I am trying to simulate an OU Process (Vasicek version) with jumps and I would like to derive the drift and diffusion term when jumps are incorporated, which will enable me to perform monte carlo ...
- 139
0 votes
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61 views
How to exactly sample two Cox-Ingersoll-Ross processes that share the same Brownian motion
Lets say that I have two CIR processes \begin{align} dX_t &= b_x(a_x - X_t)dt + s_x \sqrt{X_t}dB_t \newline dY_t &= b_y(a_y - Y_t)dt + s_y \sqrt{Y_t}dB_t \end{align} And I want to sample from ...
- 1
1 vote
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89 views
Scaled VaR: approximation vs reality
Previous question: Understanding VaR rescaling After understanding the usual VaR scaling formula $$\text{VaR}_{T,\alpha}=\sqrt{T}\text{VaR}_{1,\alpha}$$ I wanted to know by how much it deviates from ...
- 133
0 votes
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155 views
Pricing a zero coupon callable bond
Suppose I have a 20-year zero bond with a call date in 10 years and a zero interest rate of 2%, which is currently valued at a Z-spread of 100. Now I would like to evaluate the right of termination ...
0 votes
0 answers
399 views
Confusion About PFE Calculation and XVA Pricing Engine's Exclusive Reliance on Parameter Simulation
Potential Future Exposure (a credit risk metric) is calculated using $$PFE(\tau) = \text{max}\Big(0, \mathcal{P}_{derivative}(\tau) - CVA(\tau)\Big)$$, where $\mathcal{P}$ is the price / fair value / ...
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1 vote
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137 views
What are state-of-the-art methods for forecasting of rates and volatilities?
Usually forecasting is based on a model for the evolution of a value $x(t)$ based on some parameters ${\beta}$ that can then be estimated using various statistical means. For yield curves and ...
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