# Questions tagged [derivatives]

A financial contract whose payoff is linked to the evolution of an underlying security.

22 questions
Filter by
Sorted by
Tagged with
7k views

### How to estimate real-world probabilities

In the world of finance, Risk-neutral pricing allow us to estimate the fair value of derivatives using the risk free rate as the expected return of the underlyings. However, the behavior of ...
3k views

### Why discounted derivative price is a martingale?

Usually after showing that discounted stock price process is martingale under the risk-neutral measure, most authors say that this implies that the discounted derivative price process is a martingale ...
3k views

### How to use the stock as a numeraire to price a derivative with payoff of the form $(S_T f(S_T))^+$?

I have $\frac{dS_t}{S_t} = rdt + \sigma dW_t$ as usual under the money-market numéraire and I need to price options with payoffs $$(S_T f(S_T))^+$$ How do I express the stock dynamics using the ...
262 views

### What are the books in which to study the basics of the derivative financial instruments?

Books similar to Options, Futures, and Other Derivatives by John C. Hull. I need another academic book that explains the basics of quantitative finance derivatives (forward, futures, options)
707 views

### Theoretical limits for contango and backwardation

What do you think would be the theoretical limit for contango? What about backwardation? This was asked in an interview. I am still not so sure about the answer.
3k views

### Why is the SABR volatility model not good at pricing a constant maturity swap (CMS)?

I have heard that the SABR volatility model was not good at pricing a constant maturity swap (CMS). How is that?
4k views

### Why a self-financing replicating portfolio should always exist?

According to my understanding the derivation of the Black-Scholes PDE is based on the assumption that the price of the option should change in time in such a way that it should be possible to ...
1k views

### Delta Hedging with fixed Implied Volatility to get rid of vega?

I'm wondering if i should use a floating IV or a fixed IV to delta hedge my options every day. I've read this post but would like different information : Delta Hedging with fixed Implied Volatility ...
286 views

### Replicating a portfolio with a certain payoff function

Assume there are two stocks $S_1$ with price $p_1(t)$ and $S_2$ with price $p_2(t)$ where $t$ indicates time. Assume, there is a hypothetical derivative $D$, which is such that, price of $D$ at a time ...
606 views

176 views

### Why don't we take the differential to the Delta in the Delta hedge-portfolio

For option $V(S,t)$ with underlying asset $S$, we have a hedge portfolio $$\Pi = V(S,t) - \Delta(S,t)S$$ I always confuse here, when we take the differential of $\Pi$ $$d\Pi = dV -\Delta dS$$ why ...
4k views

### Long/Short Vega and Option Positions

Why do you get long vega when you buy an option and short vega when you sell an option? I would have thought that for both buying and selling options the vega would change according to whether the ...
169 views

### Upper bound option price in volatility dimension

All, I have a theoretical question about the value of an option when spot price goes to infinity as a function of volatility going to infinity. I know that for a call option: The option value ...
104 views

### Cap option on Libor

We denote discount factor $D(t),$ zero coupon bond $B(t,T),$ $E_t[X] = E[X|\mathcal{F}(t)]$ and $T$-forward measure \$E_t^{T}[\ ]....