# Tagged Questions

The tag has no wiki summary.

23 views

### Discounted Stock Price

I have the following Question : Prove that under the risk-neutral probability p the stock and the banjaccount have the same average rate of growth. In other words, if $S_0 , S_N$ are the initial ...
13 views

### Complete Multiperiod Binomial model

I have the following deifnition of a Complete multiperiod binomial model: A multi period binomial model can be called complete if every derivative security can be replicated by trading in the ...
62 views

### Using Black-Scholes to price a geometric average price call

Sorry if this is the wrong exchange for this question. It seems to be the most relevant, anyway. I'm trying to learn and understand the Black-Scholes framework, with a focus on the stochastic ...
153 views

84 views

### Differential of stochastic term

Question 1: How does one come up with the equation in the red box below? It looks like some kind product rule, but I'm not sure how to apply Ito's lemma here. Bjork doesn't seem to explain it ...
49 views

### Conditional expectation of a non stochastic process

In an example I was working through it was shown that $W_{t}^{2} - t$ was a martingale with respect to the Brownian motion filtration $\mathcal{F}_{s}^{W}$ with $t>s$. Everything was fine except a ...
216 views

242 views

### Girsanov Theorem and Quadratic Variation

Girsanov theorem seems to have many different forms. I've got a problem matching the form in wiki to the one in Shreve's book, due to the difficulty of quadratic variation calculation. Below is the ...
132 views

### FX Rate dynamics

Let's suppose USD/EUR price in USD follows a GBM with $$dS_t = rS_tdt + \sigma S_tdW_t$$ What process does EUR/USD follow in EUR?
96 views

### Stochastic Differential

Let $W_t$ be a Wiener process. It is clear to me that $dW_t$ is of size $\sqrt{dt}$. This can be seen because $$\mathrm{Var}(W_{t+\Delta} - W_{t})=\Delta.$$ But am I allowed to actually write ...
153 views

By using the canonical representation of a semimartingale in Eberlein, Glau and Papapantoleon's "Analysis of Fourier Transform Valuation Formulas and Applications", on page 3: $$H = B + H^c + h(x) ... 0answers 106 views ### PDE and Black Scholes problem Consider Black Scholes problem \frac{\partial V}{\partial t} + \frac{\sigma^2 S^2}{2}\frac{\partial^2V}{\partial S^2} + rS\frac{\partial V}{\partial S} -rV = 0 with boundary condition V(S,T)=f(S), ... 2answers 171 views ### Uniqueness of equivalent martingale measure in Black Scholes-Model Let's consider standard Black-Scholes model with price process S_t satisfying SDE$$dS_t = S_t(bdt + \sigma dB_t)$$, where B_t is standard Brownian Motion for probability \mathbb{P}. I ... 1answer 197 views ### What is a good Computer Algebra System for financial engineering? I would like to know if there exists some computer algebra systems adapted to calculate pricing based on particular models, i.e. pricing YoY Inflation Swap under Jarrow Yildirim Model. I know that ... 3answers 208 views ### Show that E[B_t|\mathscr{F}_s] = B_s Given prob space (\Omega, \mathscr{F}, P) and a Wiener process (W_t)_{t \geq 0}, define filtration \mathscr{F}_t = \sigma(W_u : u \leq t) Let (B_t)_{t \geq 0} where B_t = W_t^3 - 3tW_t. ... 3answers 188 views ### Determine E[W_p W_q W_r] Given prob space (\Omega, \mathscr{F}, P) and a Wiener process (W_t)_{t \geq 0}, define filtration \mathscr{F}_t = \sigma(W_u : u \leq t) Let 0 < p < q < r. Determine E[W_p W_q W_r]. ... 2answers 209 views ### Filtration and measure change I asked this question in math stackexchange but to no avail. So i'm trying the luck here. I'm reading Steven E. Shreve's "Stochastic calculus for finance II", and find myself not really understand ... 0answers 44 views ### Intensity Function of Stochastic Processes I'm fitting some financial data to a model based on a stochastic process and evaluating the fit of it by looking at the compensator. However, I cannot understand well what does it mean to take the ... 1answer 113 views ### Explicit solution SDE I have the following SDE:$$dY_{t}=A\left(\frac{W_{t}^{1}}{\sqrt{t}},\frac{Y_{t}}{\sqrt{t}}\right)dW_{t}^{1}+B\left(\frac{W_{t}^{1}}{\sqrt{t}},\frac{Y_{t}}{\sqrt{t}}\right)dW_{t}^{2}$$where ... 1answer 71 views ### Discounted risky asset stochastic process problem S_t is the random variable representing the risky asset price at time t. M_t is the riskless asset. They are governed by the equations \frac{dS_t}{dt}=\mu dt + \sigma dZ_t and dM_t = rM_t ... 2answers 217 views ### question on Leif Andersen's “Interest Rate Modeling, vol 2 Term Structure Models” I'm reading Leif Andersen's "Interest Rate Modeling, vol 2 Term Structure Models" and met a problem on Chapter 14 LM Dynamics and Measures, \S 14.2.5 Stochastic Volatility, Lemma 14.2.6, on page ... 2answers 280 views ### Why does the price of a derivative not depend on the derivative with which you hedge volatility risk? I'm trying to derive the valuation equation under a general stochastic volatility model. What one can read in the literature is the following reasoning: One considers a replicating self-financing ... 6answers 785 views ### Self-financing and Black-Scholes-Merton formula Self-financing is an important concept in financial product replicating, normally used in pricing. I read about several ways to derive Black-Scholes-Merton (BSM) formula. Seems some approaches ... 1answer 187 views ### Trading over a Ornstein/AR process For a OU/AR(1) process is there anyway to analytically calculated most probable period of time the process is likely to diverge from the average, before turning to converge. Basically I am looking ... 2answers 322 views ### SVCJ (SVJJ) Duffie et. al Model implementation in Matlab I'm attempting to implement aforementioned SVCJ model by Duffie et al in MATLAB. so far without success. It's supposed to price vanilla (european) calls . parameters provided, the expected price is: ... 1answer 373 views ### How to get Geometric Brownian Motion's closed-form solution in Black-Scholes model? The Black Scholes model assumes the following dynamics for the underlying, well known as the Geometric Brownian Motion:$$dS_t=S_t(\mu dt+\sigma dW_t)$$Then the solution is given: ... 2answers 243 views ### How to compute \mathbb{E} \left[ (W_s + W_t - 2W_0)^2 \right]? The solution to the SDE$$dx_t= -kx_t dt + cx_t dW_t$$is$$x_t = x_0 e^{\left(c - \frac{k^2}{2} \right)t}e^{-k W_t}$$with mean$$\mathbb{E} \left[ x_t \right] = x_0 e^{\left(c - ...
Here I have this question (i) state Ito's formula (ii) hence or otherwise show that $\int^t_0B_s dB_s = \dfrac{1}{2}B^2_t -\dfrac{1}{2} t$ (iii) define the quadratic variation $Q(t)$ of Brownian ...