Linked Questions

0 votes
0 answers
37 views

Risk Neutral Pricing - Why the Risk Free rate for Risky security (Intuition) [duplicate]

I am struggling with this concept of risk neutral probabilities. My understanding of how a risk neutral pricing framework works is as follows: (discrete, binomial lattice for simplicity) I do not know ...
Jaimeblt1's user avatar
47 votes
16 answers
34k views

Why Drifts are not in the Black Scholes Formula

This question has puzzled me for a while. We all know geometric brownian motions have drifts $\mu$: $dS / S = \mu dt + \sigma dW$ and different stocks have different drifts of $\mu$. Why would ...
CuriousMind's user avatar
49 votes
8 answers
51k views

How does the "risk-neutral pricing framework" work?

I've struggled for a long time to understand this - What is this? And how does it affect you? Yes I mean risk neutral pricing - Wilmott Forums was not clear about that.
Jack Kada's user avatar
  • 809
5 votes
7 answers
3k views

Why don't real-world probabilities affect the price of a call in a 1-step binomial model?

I was a bit hesitant to post this question because it seems so basic...but I wasn't able to figure it out on my own. Say we setup a one-step binomial tree with $S_0=100$, $S_u=110$ and $S_d=90$, ...
Karim L's user avatar
  • 118
7 votes
2 answers
861 views

Why does the diffusion term remain the same when we change pricing measure?

Consider some Itô process $dS(t)=\mu(t)dt+\sigma(t)dW^{\mathbb P}_{t}$ under the measure $\mathbb P$, where $W^{\mathbb P}$ is a $\mathbb P$-Brownian motion In plenty of interest rate examples, I have ...
user9078057's user avatar
3 votes
1 answer
1k views

Risk Neutral Valuation, Drifts and Calibration

Lets consider a pricing model like Vasicek. Apparently, if you calibrate a derivatives pricing model to market prices this gives you risk neutral parameters. Its not clear to me as to WHY this will ...
Trajan's user avatar
  • 2,492
1 vote
1 answer
1k views

Power Options & Forwards on Stock Squared

Short story: the process for Stock price squared is not a martingale when discounted by the money-market numeraire under the risk-neutral measure. How can we then compute derivative prices on $S_t^2$ ...
Jan Stuller's user avatar
  • 6,098
0 votes
1 answer
1k views

Quant Interview - Options pricing [closed]

I am fairly new to all this, merely read the first few chapters of "The Concepts and Practice of Mathematical Finance". I recently had a job interview and was asked a simple question about ...
Filipe Miguel's user avatar
2 votes
1 answer
627 views

Real world probabilities from option implied risk neutral density?

The work of Breeden and Litzenberger-formula (https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2642349) gives us a risk neutral probability distribution of a stock price, depending on the option ...
Lejoon's user avatar
  • 147
0 votes
1 answer
563 views

What is delta of an option signaling?

In an interview I was once asked what the delta of an option was and my answer started from the fact that it is the first derivative of the option with respect to the price, and then I concluded ...
Mining's user avatar
  • 165
1 vote
1 answer
197 views

Risk-Neutrality: Discount factors of the $P$ world according to risk preferences?

I am coming to terms with the connections between the so-called $P$ world and the $Q$ world. In my understanding, the risk-neutral measure $Q$ induces a probability space under which investors are ...
MinaThuma's user avatar
  • 459
0 votes
1 answer
221 views

option pricing: monte carlo simulations that include expected return [closed]

In the book Derivatives Markets (McDonald, 3rd edition), there's a chapter on Monte Carlo valuation of option prices. It starts with simulating stock prices (p578) with the following equation: ...
MikeD's user avatar
  • 11
0 votes
0 answers
171 views

Real Option Valuation using simulation: real world vs risk neutral measure

I am trying to value a real option in the form of a software investment using a simulation. The software investment yields to daily revenues $R_t$ and costs $C_t$. Here are the formulas for these: $$...
Arely's user avatar
  • 1
0 votes
0 answers
73 views

How to access the Black Sholes Formula through the Distributive Law?

Recently I read a comment on how to interpret the Black Sholes Formula and more specifically how to wrap your head around the d1/d2. Although there were many good comments, this one stood out when one ...
Telefondemonen_se's user avatar