Questions tagged [stochastic]
The stochastic tag has no usage guidance.
72
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Financial Time-Series: Stochastic or Dynamic?
I have learned how some methods of constructing predictive models of financial time-series involves assumptions of stochasticity. For example, reinforcement learning utilizes the Markov Decision ...
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66
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Confusion about how price of a contingent claim at time 1 could give arbitrage
I have been reading the book Tomas Bjork's Arbitrage Theory in Continuous Time and could not understand how there could be arbitrage if the price of a contingent claim is not $X$.
To give some ...
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Heston Model Sensitivity Qualitative Property
Consider the following Heston model:
$$\begin{aligned}
\mathrm{d}S_t&=rS_t\mathrm{d}t+\sqrt{v_t}S_t\mathrm{d}B_{1,t}\\
\mathrm{d}v_t&=-\kappa(v_t-\bar{v})\mathrm{d}t+\sigma_v\sqrt{v_t}\mathrm{...
- 21
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Aggregate Yield to Maturity with Stochastic Interest Rate Paths
Suppose I am valuing a callable bond using stochastic interest rate paths (LMM generated for example) and I wish to express yield to maturity as a single value.
Would it be appropriate to average the ...
- 103
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Can Heston volatility model be used to calculate VaR or CVaR?
I'm just a beginner and third-year statistics major student. Based on what I read in some journal, most common model that used to calculate VaR or CVAR is GARCH. Is there any possibility that I can ...
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150
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Expectation of the realized volatility
I was reading Zhang and Wang 2023 and I have some doubts regarding it. The realized Stochastic Volatility Model is expressed as follows:
$$\begin{matrix}
y_t = \exp \big( \frac{h_t}{2} \big) \...
- 127
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How does the inclusion of stochastic volatility in option pricing models impact the valuation of exotic options?
Been lurking this forum for quite some time and there’s this concept I can’t wrap my head around:
How does the inclusion of stochastic volatility in option pricing models impact the valuation of ...
- 33
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253
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Necessary conditions to ensure that stochastic integral is a normal variable
Let $\left(W_t\right)_{t\geq 0}$ be a Brownian motion with respect to filtration $\mathbb{F}=\left(\mathcal{F}_t\right)_{t\geq 0}$. Let $\left(\alpha_t\right)_{t\geq 0}$ be an $\mathbb{F}$-adapted ...
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Calibration of Local or Stochastic Volatility Models to Prices vs Implied Volatilities
As the title suggests, what is the difference between calibrating an option pricing model (say the Heston model) to market option prices instead of computing their implied volatilities using Black-...
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Derive the Probability of Default (PD) of private companies with Merton Model
Do you know a well used method how to calculate the PD of private companies using the Merton Model.
The main challenges I am facing is to get the appropriate volatility of the assets and the drift.
...
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4th Order Brownian Motion Martingale [closed]
I understand the first order MG of brownian motion is Bt.. the second order is Bt^2 - t and the third order is bt^3 - 3tBt. How can I find the fourth and beyond order of a Brownian Motion Martingale?
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What does a non-stochastic limiting shrinkage function mean?
I'm reading the paper "The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation" by Ledoit and Wolf (2020). When a function that is used to transform the ...
2
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1
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341
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Simple Black-Scholes alternatives
I work at an accountancy firm and we use Black-Scholes to value equity in private companies that has option like features. The equity we typically value is akin to deeply out of the money European ...
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Integral of Function of Brownian Motion w.r.t Time (Context: Computing Quadratic Variation)
I am looking to compute the quadratic variation of $$S_t = S_0e^{\sigma B_t}$$ where $B_t$ is Brownian Motion. Applying Itô's lemma, I having the following
$$(dS_t)^2 = S_0^2\sigma^2e^{2\sigma B_t}dt$$...
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104
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Sum of discretely sampled BM
If an underlying follows lognormal GM with no drift $dS_t = \sigma S_t dW_t $ and $A_N = \Sigma_{i=1}^{N} S_{t_i}$. How to compute variance of $A_N$?
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