Questions tagged [pricing-formulae]

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Formal proof for risk-neutral pricing formula

As you know, the key equation of risk neutral pricing is the following: $$\exp^{-rt} S_t = E_Q[\exp^{-rT} S_T | \mathcal{F}_t]$$ That is, discounted prices are Q-martingales. It makes real-sense ...
4k views

How to obtain true probabilities from Black-Scholes?

How to obtain true probabilities from Black-Scholes option pricing equation? Suppose, that we know risk adjusted discount rate for the underlying asset (the drift term in the physical measure) and ...
571 views

Is it possible to demonstrate that one pricing model is better than another?

Take the classic GBM (geometric Brownian motion) model for equities as an example: ds = mu * S * dt + sigma * S * dW. It is the basis for the classic Black-...
6k views

Predicting Price Movements on a Betting Exchange

On a betting exchange the price (the odds that an event will happen expressed as a decimal, 1/(percentage chance event occurring) of a runner can experience a great deal of volatility before the event ...
4k views

Market Value of a CDS

I need to model the market value of CDS in a portfolio. My current approach is to calculate the present value of the future spread payments - does anybody have a better idea to solve the problem? ...
691 views

Is there a comprehensive reference book on US fixed income conventions?

In Canadian fixed income markets there is a nice handbook called Canadian Conventions in Fixed Income Markets (PDF). It contains detailed market standard pricing formulas for calculating prices, ...
492 views

How do bond pricing formulae differ between the US, UK and the Euro zone?

Let's restrict the scope of the question a little bit: I'm interested to learn about major differences in pricing formulae for nominal government bonds. The pricing formulae for inflation-linked bonds ...
3k views

Documentation of the ISDA CDS standard model

I have to validate the use of the ISDA CDS standard model. Don't understand me wrong - I am sure that the ISDA model is "good" I just need to know what it is in detail. I can download an Excel-...
634 views

How do equivalent martingale measures arise in pricing?

I'm studying for an exam in financial models and came across this question: "An agent with $C^2$ strictly increasing concave utility $U$ has wealth $w_0$ at time 0, and wishes to invest his wealth in ...
357 views

What is a good Computer Algebra System for financial engineering?

I would like to know if there exists some computer algebra systems adapted to calculate pricing based on particular models, i.e. pricing YoY Inflation Swap under Jarrow Yildirim Model. I know that ...
361 views

Foward-start option pricing

Consider a probability filtred space $(\Omega, \mathcal F, \mathbb F, \mathbb P)$, where $\mathbb F = (\mathcal F_t)_{0\leq t\leq T}$ satisfing the habitual conditions and is generated by $1 d$- ...
105 views

Why do we need approximation in option pricing?

We know that we can get a closed form for European option price. And we can calculate directly the normal distribution accumulation. But I saw that people use many approximation methods such as ...
13k views

Formula for forward price of bond

What is the formula for the forward price of a bond (assuming there are coupons in the interim period, and that the deal is collateralised) Please also prove it with an arbitrage cashflow scenario ...
327 views

Dupire's formula proof

I just have a question for the beginning of a proof: Suppose $\frac{dS_{t}}{S_{t}}=(r_{t}-q_{t})dt+\sigma(t,S_{t})dW_{t}$ with $r,q,S$ stochastic. In the book I read, it is written: We define the ...
5k views

What is the Most Efficient Way to Calculate the Internal Rate of Return IRR?

I have built a program that prices financial assets and it does this in part by calculating the IRR. The problem is that it does not run as quickly as I would like it to. I currently use the Newton-...
424 views

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in long term options on equities, what is the greek used for security lending rate, and what formula do you use?

in long term options on equities, what is the greek used for for security lending rate, and what formula do you use? would it often move contrary to moves in risk free (ois) and so in practice is it ...
180 views