# Questions tagged [itos-lemma]

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### Discreet-time stochastic difference equation and Ito thorem

In continuous time, when we want to find the dynamics of a function of a stochastic process, we need to use Ito's lemma which gives an "extra"" term for the drift. What if we are in discreet time and ...
74 views

### Differential of time over Browninan motion

I know that $\frac{dW_t}{dt}$, with $W_t$ a brownian motion, does not exist. However, does $\frac{dt}{dW_t}$ exists? Or does it even make sense? I am trying to calculate the quotient of two ...
62 views

### understanding of Ito's lemma applied to stock price?

I am currently reading John Hull's book and am a bit confused about the Ito's lemma when it is applied to the stock price. Given $dS=\mu Sdt+\sigma Sdz$, by applying Ito's lemma to $G=\ln S$, we have ...
221 views

### Black and Scholes equation for portfolio **with** arbitrage

I am well aware of how the ordinary Black and Scholes equation is derived, under the assumption of an arbitrage free portfolio, $V=G-hS$. Here $S$ is the price of the underlying and $G$ is the option ...
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146 views

### Solving Stochastic Differential Equation for Geometric Brownian Motion with time-dependent drift

Given the stochastic differential equation: $$dZ_t = -Z_t \theta_t dB_t, \quad Z_0 = 1.$$ for an adapted process $\theta_t$ and Brownian motion $B_t$, how exactly do I apply Itô's Lemma to obtain: ...
65 views

### Relating two equations in a jump-diffusion process

I am trying to understand an argument involving the pricing kernel $\xi_t$ in the context of a simple jump diffusion model for the price of an asset $S_t$: \begin{align} \xi_t = \exp \left[ -\theta ...
144 views

### Partial derivative of Ito integral without product rule

I'm thinking about the problem of deriving the stochastic differential of an integral with both time and state part of the integrand but not in a way that you can easily factor it out - for example I ...
107 views

### How To Understand the Drift of ln(S) if S Follows Geometric Brownian Motion

As we know, if an asset S follows geometric Brownian motion, under risk neutral measure, it can be expressed as $\frac{dS}{S}=rdt+\sigma dW$, by applying Ito's lemma, $d(lnS)=(r-0.5*σ^2)dt+σdW(t)$, ...