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Black-Scholes is a mathematical model used for pricing options.

0 votes
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Continuous Time Asset Model in Higham

$\delta t \rightarrow 0$ as $n\rightarrow \infty$. In that limit jumping to 0 is probability 0 with a continuous diffusion model. In the discrete case it is a numerical possibility but more of the a …
  • 2,137
0 votes
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Monte Carlo simulated price and Black Scholes Price are giving a huge difference in my Matla...

Given the formula for S, the variable phi should be a normal standard variable, not with stdev sigma.
  • 2,137
2 votes

Is there a good closed-form approximation for Black-Scholes implied volatility?

Peter Jaeckel methods from the papers mentioned are the industry standard used by most practitioners to get IV. In addition in practice the article you mention is probably of very little use because …
  • 2,137
9 votes
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Positive theta on a long put?

If a european option value becomes lower than intrinsic value it gets negative time value. In this circumstance the theta becomes positive because as time approaches to expiry the option value has to …
  • 2,137
6 votes

Can you model the LIBOR rate as a geometric Brownian motion?

It is not reasonable because rates display a stationarity but brownian motion is not stationary. The variance of libor at a future time $t>0$ conditional on the value at time $t=0$ does not scale as …
  • 2,137
2 votes

Why does a higher stock value imply a higher call option value

Instead of talking about an option you should apply your reasoning to the simpler example of the forward contract to see the flaw in your argument. Suppose the spot is a martingale process and suppos …
  • 2,137
1 vote
Accepted

Interpretation of IV and its use in stock movement prediction

The Bachelier model which assumes that price follows a normal distribution is a correct approximation for the Black-Scholes one for short times t. When time is short it's fine to ignore drift because …
  • 2,137
1 vote

Why Drifts are not in the Black Scholes Formula

I believe the simplest way to understand this intuitively is to look at the case of the forward contract instead of an option. If the drift of the stock is higher should not the forward be higher ? No …
  • 2,137
1 vote

Discounted asset price is martingale in BS model

First of all, it is part of the Ito formula theorem that if $S_t$ is an Ito process then $V(t,S_t)$ is also an Ito process. This includes the regularity property you mention for the integral you menti …
  • 2,137
1 vote

What are the underlying events that the random variables map to the real line in the derivat...

In probability theory $\Omega$ is called the « sample space » of possible outcomes. It does not have an actual representation and it does not matter much since the only thing that really matters is th …
  • 2,137
1 vote
Accepted

Binomial Tree Option Pricing Model. Lets talk dividends and futures

1) First of all many future option contracts are European, so for those there's no modeling problem. Just use BS. Now certain contracts like quarterly ES option are american for historical reasons 2) …
  • 2,137
0 votes

Tracking error Black Scholes

If the trader is short the call then the pnl of her delta hedged portfolio is made of the theta rent which is positive and accrues at the implied volatility $\sigma^*$ times dollar gamma and and the s …
  • 2,137