Questions tagged [simulations]

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1answer
37 views

Correct way to calculate interest rate volatility for risk calculations

I'm trying to include interest rate derivatives in some Value at Risk calculations and am having trouble getting trustworthy values. My current approach is to look at the appropriate risk factor for ...
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0answers
12 views

How to simulate the cross-section

I am looking to simulate the whole cross-section of daily return series for 20 to 60 days. The purpose is to test some risk measures based no maximum drawdown. Thus, it needs the whole time series. ...
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0answers
28 views

Simulated VaR with differently distributed processes

I am attempting to calculate the one-month 95th and 99th percentile profits for a two-year portfolio of energy-generating assets over the next three months. This means that the calculation has two ...
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1answer
63 views

Can a portfolio value consisting of longing a delta shares of stocks and shorting a call option greater than strike price?

While trying to implement Black-Scholes delta hedging for a European call option using Python, I came across the following phenomena: Given a portfolio consisting of longing a delta shares of ...
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0answers
87 views

Is there a simplified framework to consider for modelling the stock market?

Does anyone know a reference where one can read up on different aspects of modelling when simulating the stock market? i.e what is known as "stylized facts" and which of these fact that are more ...
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1answer
82 views

Which metric is most predictive: Mean, Sharpe, Calmar, …?

Suppose you have created a new trading algorithm: by varying the params of the algorithm, you get a large number of similar trading strategies (e.g. slightly different trigger thresholds, stop loss ...
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0answers
61 views

Anyone got references where we can find examples of codes for agent-based simulations of financial markets?

I'm looking for references with codes for trying out simple agent-based simulations for modeling financial markets. I mostly worked with MATLAB and R, but I know a bit of python and I am learning C++ ...
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0answers
18 views

Fixed rate bond historical simulation

I am using the QuantLib library to determine the historical simulation prices of a fixed rate bond. The idea behind my simulation is to use the spot curve as driver of the bond price. Let $\{y^{j}(t)\...
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1answer
56 views

Sample path simulation using two random variables

I was wondering if there is a way of generating a sample path of a Geometric Brownian Motion using two independent standard normal random variables instead of just one. The exact scheme that uses ...
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0answers
24 views

Degree of freedom input for Monte Carlo simulation of asset returns with multivariate t distribution

How do I calculate or estimate the degrees of freedom in order to perform a Monte Carlo simulation of asset returns with multivariate t distribution using R functions? I am able to calculate the mean ...
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2answers
64 views

Is it possible to build a computer model to simulate a market to prove whether efficient theory is true or not?

I know this may sound stupid. But I had this idea and wanted to try it out for a college project. Has this been done before? If and what's wrong with this idea?
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0answers
15 views

CVA for a portfolio of long and short options

I am looking to estimate the CVA/DVA for a portfolio of options. For simplicity sake, let's assume there are two FX options in the portfolio, one long and one short. Both options have the same ...
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0answers
12 views

Finding fifth and sixth polynomials for Headrick (2002) method for non-normal multivariate distribution

I am trying to perform a 3-asset class return Monte Carlo simulation. As the asset class returns are non-normal, I found the following function rHeadrick from the ...
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0answers
32 views

Building up an Economic Scenario Generator [closed]

I am trying to build an Economic Scenario Generator in VBA or Python. Can anyone please help me with some good resources which I can follow or some basic procedures which explains how to go about in ...
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2answers
78 views

What is actually going on in Monte-Carlo simulation for Mortgage backed securities?

I just wanted to clear somethings up when it comes to pricing Mortgage backed securities using Monte-Carlo methods. I understand that interest rate paths have to be modelled in order to come up with ...
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0answers
20 views

Decision making framework for trading consumption assets in a forward exchange market

I am working on a forward market with limit order books. My idea is to illustrate market operations and trading behaviors through discrete event simulation. Consumption assets are traded in the market,...
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1answer
94 views

why does monte carlo simulation become less accurate as volatility increases? [closed]

I simulated sample paths to approximate the price of a vanilla European call and then plotted a graph comparing this to the value achieved from the Black Scholes. Why do these values diverge as the ...
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0answers
36 views

ES using historic simulation

Why is the data obtained from 91-100 days all eliminated from the calculation of the 1-day 95% ES? My interpretation is because the first day to calculate the 95% ES should be the 90th day? But I can'...
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1answer
103 views

Simulation Heston Model, markovianity

I am trying to simulate the instanteneous volatility of a Heston process. My equations are the following : wealth process: $$dX_t = r_t X_t + \theta \sqrt {V_t} u_t dt + u_t dW_{1t}$$ Volatility: $$...
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1answer
111 views

Formula for quantiles of swaprates in the 1-factor Hull-White model

Is there a closed formula to approximate the quantiles of swaprates in the 1-factor Hull White model? Background The Hull-White is a Gaussian model for the short rate. Its mean and covariance ...
1
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1answer
337 views

Difference between cross-validation, backtesting, historical simulation, Monte Carlo simulation, bootstrap replication?

To determine if a strategy is better than others, or to optimize the parameters of a model, the following statistical techniques are often employed, often one over the others instead of altogether. ...
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2answers
672 views

Risk Neutral and Real World Valuations using Monte Carlo

Assume I'm an investor that wants to sell exotic put options. No one else is selling my kind of put option, so I need to determine my own "Market Price" through Monte Carlo simulation. I know that by ...
2
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1answer
102 views

What is the annualized realized volatility of simulated Brownian motion paths?

I saw this following question in an exam. Take a Brownian motion simulation with drift 5% and annualized volatility of 20% for a period of 1 year. Then the annualized realized volatility of the ...
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1answer
55 views

Negative Libor Simulation

Can LIBOR rates be simulated using short rate models? If no, what is the reason behind it? What is a simple model to simulate LIBOR rates? Especially in a negative rate environment.
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1answer
101 views

Zero-coupon bond price under Rendleman-Bartter Model

let's say that I have simulated the interest rate using the Rendleman-Barttermodel, (which is not the best for rates I know) and then I want to simulate paths for the bond paying 1 at maturity: $$...
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0answers
31 views

Why do simulation schemes have difficulty in pricing options with low spots?

If you apply a simulation Scheme (log-Euler discretization, Euler discretization and even more advanced ones) on for instance SABR and other models, then they price a call option (where we can easy ...
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1answer
123 views

Simulation scheme for SABR beside the standard Euler discretization

QUESTION: Beside Euler Scheme, is there another more robust (and preferably easy to implement) way to simulate asset path with SABR dynamics? Simulation that will withstand even for high volatilities....
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0answers
95 views

Simulating volatility process in the Heston model using the relation between the CIR Process and Ornstein–Uhlenbeck processes

I am trying to simulate the volatility process in the Heston model using the relation between the CIR Process and Ornstein–Uhlenbeck processes. In fact, giving $\mathbf{X}$ a $n$-dimensional vector ...
5
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2answers
362 views

Simulating from a multivariate clayton copula

I am recently into copulas for finance, I've read several examples of how to generate dependent random variables with most kind of copulas. The problem for me is that all the books describe the case ...
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0answers
59 views

Pricing call option on bond under CIR model by simulating noncentral chi square distribution

In the original paper of CIR model, there is a pricing formula about call option on bond $$ \begin{array}{l}{C(r, t, T ; s, K)} \\ {=P(r, t, s) \chi^{2}\left(2 r^{*}[\phi+\psi+B(T, s)] ; \frac{4 \...
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5answers
2k views

Python libraries for Monte Carlo simulations?

I am learning about monte carlo simulations and I have found many blogs explaining its implementation in python. Because its a widely known and an important technique for structuring asset prices. I ...
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1answer
220 views

Historical Simulation of Bond, Stock and Option Portfolio

If I have a portfolio consisting of 1-one stock of unit price equal to S, 2-one 9% coupon American bond with 20 years to maturity and a par value of $1000, 3-and one European call option on the ...
2
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0answers
102 views

Jump Diffusion Model - Volatility and Mean of Jumps

I am trying to understand the concept of jump diffusion model. So far what I've understood is that by adding a Jump parameter to a GBM (Geometric Brownian Motion) we can generate a Jump diffusion ...
2
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2answers
1k views

Monte Carlo simulations in Python using quasi random standard normal numbers using sobol sequences gives erroneous values

I am trying to perform Monte Carlo Simulations using quasi random standard normal numbers. I understand that we can use sobol sequences to generate uniform numbers, and then use probability integral ...
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1answer
74 views

Simulating stock prices with and without intermediate paths

So I am simulating stock prices with what I believe to be geometric Brownian motion using parameters from the usual Black-Scholes framework (Please correct me if I am wrong) with the following formula:...
2
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0answers
48 views

Negative theta in Log-linear stochastic volatility model

I was asked to simulate the following geometric Brownian motion to get paths for the SPX stock price. the process follows a Log-Linear stochastic volatility. $dS_t = \mu S_tdt+e^VS_tdW_1 $ where ...
3
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1answer
225 views

Why is it more accurate to simulate ln(S) rather than S?

Let's take a process $S$ that satisfies: \begin{equation} dS = \mu S dt + \sigma S dz \end{equation} with $dz$ a Wiener process, $\sigma$ the volatility of $S$, $\mu$ the expected return of $S$. From ...
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0answers
492 views

Longstaff-Schwartz, special american option simulation using Python (numpy package)

I got a put option, which can be exercised 3 times, all at different times, which are each month of a year $$t_1 = \frac{1}{12}, t_2 = \frac{2}{12} ... t_{12} = 1$$. Respectively, if exercised at $$...
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1answer
192 views

Simulated Sharpe Ratio Calculation for Leveraged Portfolio

I've written some VBA code to simulate the effect of borrowing money, investing it, and repaying the loan daily. PseduoCode: Start with a portfolio value of P = 1 Each day borrow P, invest 2*P, ...
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1answer
2k views

Shifted Log-Normal model

I am trying to understand how the shifted log-normal model works, in which we shift a log-normal model by a factor before the simulation so that interest rates don't turn negative during the ...
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0answers
28 views

Why no prepayment fee for the reverse mortgage?

I am currently studying the costs (to lender) of adding certain additional options to the reverse mortgage, including the option of prepayment. Would there be any scenarios of housing price/mortgage ...
1
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1answer
460 views

negative values in geometric brownian motion

A GBM $ \frac{dx}{x} = \mu dx + \sigma dW $ solves to $x_t = x_o e^{(\mu - \sigma^2)t + \sigma W_t}$ From the solution, it is clear that $x_t$ cannot become negative. However, it is not so clear ...
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1answer
284 views

Single vs Multi factor interest rate model

How do we explain the difference beween a single and multi factor interest rate model. Short term interest rate is one of the factor which is used in drift and vol calculation but what are other ...
2
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1answer
177 views

Merton's Jump diffusion model: Specify poisson rate

Currently applying the Merton's jump diffusion to test how Option price change as parameters change. However, I am struggling to specify the poisson rate $\lambda$. We know that: $P(\text{There is a ...
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0answers
154 views

Multivariate Hawkes Process Simulation

I am trying to implement Ogata's thinning algorithm to simulate multivariate Hawkes Processes in Python (the algorithm can be found here: https://www.math.fsu.edu/~ychen/research/Thinning%20algorithm....
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1answer
160 views

Simulating assets of different currencies

I have a situation as follows: One year call option on a Euro stock with a Euro denominated strike. Knock in feature as follows - The option can only pay out if the growth in the Euro stock over ...
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1answer
49 views

In CVA simulation, timesteps vs number of simulations?

On a CVA system with limited computational power. For pricing, What is best, More timesteps and less number of simulations or less timesteps and more number of simulations? for example with a whole ...
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0answers
23 views

Simulating Taxed Equity Return Series (U.S.)

I'm looking to learn how to correctly simulate taxes on dividends and capital gains on simulated return series for U.S. Equities with dividend reinvestment. I understand I will have to keep track of ...
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2answers
125 views

Distribution of data for GBM

I am running some Monte Carlo simulations with GBM on time series of commodity prices. First of all, the price data is annual between 1900-1950. I would firstly like to know if it is bad practice to ...
1
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1answer
94 views

Simulating trading strategies

I want to simulate real time trading strategies. For simplicity, let's say I only want to simulate a long-only portfolio on S&P500. I have a couple of questions: Is there a place online where ...