The tag has no usage guidance.

learn more… | top users | synonyms

1
vote
1answer
35 views

Merton portfolio allocation problem proportions/weights >1 or <0?

In the classical Merton portfolio problem, lets assume: $$ dX_t \, = \, \frac{\pi_t X_t}{S_t} S_t(\mu dt +\sigma dW_t) = \pi_t X_t (\mu dt +\sigma dW_t) $$ ie: zero interest rates for simplicity. ...
2
votes
1answer
130 views

Problem with derivating integral

I have a doubt : I know that if $x_{t}=\int_{0}^{t}\gamma(s)dW_{s}$ (with $W_{s}$ a brownian motion), we have : $dx_{t}=\gamma(t)dW_{t}$ What about if $x_{t}=\int_{0}^{t}\gamma(s,t)dW_{s}$. Do I have ...
3
votes
3answers
107 views

existence of implied volatility

I read a book where it was written : 1/ "implied volatility is the market's consensus on the volatility of the asset between now and the maturity of the option". -> Could someone explain me this ...
3
votes
2answers
443 views

Is it really possible to create a robust algorithmic trading strategy for intraday trading?

I'm an engineer doing academic research for my master thesis in the area of quantitative finance, basically the purpose is to study the possibility to create an intraday-trading algorithm. I've tried ...
3
votes
2answers
126 views

Intergral of Brownian motion w.r.t. Brownian motion

I don't understand why $S$ (highlight on picture), I learned $$\int_0^t W(s) dW(s) = \left. \frac{1}{2} (W^2(s)-s) \right \vert_0^t $$ everyone please explain for me. Thank you
4
votes
1answer
92 views

Why $W_{t}^3$ is not a martigale?(by Definition)

If $W_t$ be a wiener process then,how can i show that $W_{t}^{3}$ is not a martingale by definition?
3
votes
1answer
108 views

stochastic calculus - brownian motion

I don't know how to prove this : let be $X_t = \int_{0}^{t}\sigma_{u}dW_{u}$ where $\sigma_{t}$ is a predictable process. If $|\sigma_{t}| = c$ a.s. how can I prove that $X_{t}=c*\beta_{t}$ (...
1
vote
1answer
125 views

stochastic calculus - Itô formula?

I encounter a problem in the proof below: I don't know how to proove the first line in yellow (cf below): it makes me think about the Itô formula a lot I don't undertand the deduction (ok $\gamma^{\...
2
votes
1answer
58 views

equality in distribution

I encounter the following problem : I have the equality in distribution: for all $\lambda >0, ((1/\lambda)*\int_{0}^{\lambda t}\sigma_{u}^{2}du,t\geq0)=(\int_{0}^{t}\sigma_{u}^{2}du,t\geq0)$ ...
2
votes
1answer
61 views

forward option, stochastic calculus

I encounter a problem to understand this: The price of a forward option is : $C(K,t,T)=\mathbb{E}[((S_{T}/S_{t})-K)+]$ OK The option should only depend on $T-t$ because the yield randomness (for a ...
1
vote
3answers
368 views

How to differentiate a brownian motion?

By definition a wiener process cannot be differentiated. But when we use Ito's lemma on F = X^2, where X is wiener process we have total change in ...
0
votes
0answers
53 views

What interest rate dynamics would you suggest to simulate a single swap?

I need to calculate the Potential Future Exposure (PFE) for a single swap (not a portfolio). As far as I know, a stochastic model is needed to simulate the interest rate curves (from here). Could ...
0
votes
0answers
118 views

Stochastic Volatility for Stocks, FTSE

Can someone help me with calculating Stochastic Volatility (of stocks and options) using SAS or R or Matlab please? I am new to SAS and I am trying to use Heston model, White-Hull model or any other ...
1
vote
0answers
55 views

What are the estimation methods for SV models?

I want to know about some methods like Methods-of-Moments, Quasi-Maximum Likelihood method, Baysian methods using Markov Chain Monte Carlo methods. Is there any reference to have an idea of these ...