# Tag Info

## Hot answers tagged pricing-formulae

Accepted

### Formula for forward price of bond

Amazingly, there are several different methods for computing bond forward price – the underlying ideas are the same (forward price = spot price - carry), but the computational details differ a bit ...
• 11.8k
Accepted

### Stochastic volatility

[Short answer] No closed-form formula in general. You need to resort to numerical methods. Monte Carlo is preferred by most practitioners but you could also use Finite Difference schemes (and ...
• 14.7k

### How to price a phoenix and snowball type autocallable options?

Typically structures like this are traded as notes. They will be sold at a face value of 100%, where that is normally the combination of a zcb (ie 1y usd, say 97.5%), expected coupon (say +10%), short ...
• 2,581

### Valuation of a swap where both parties can cancel (not settle at market) with accrual method instead of present-value?

Any time that a contract is cancellable by either party, it will be cancelled. That's because it is always to one party's advantage to cancel rather than carry on. The exception is that the contract ...
• 17.2k

### Are there really closed-form pricing formulas?

In fact, the frontier between closed formulas and "opened" ones is a litle bit fuzzy. In fact, as soon as you use special functions like log, exp, erf, erfc and so on, you are relying on ...
• 51

### Are there really closed-form pricing formulas?

It typically means one can price the option in terms of a "simple" formula as opposed to having to resort to numerical methods such as Monte-Carlo, numerical PDEs, numerical integration, ...
• 394
Accepted

### Pricing of forwards contracts

Decompose the first formula as $F_0=(S_0 - S_0(1-e^{-dT}))e^{rT}$ then let $PV_{I} = S_0(1-e^{-dT})$ which represents the present value of dividends (dividend rate = $d$) paid on the security during ...
• 5,672

### Is the pricing formula for FX Forwards the same for FX Swaps?

Yes. The swap is quoted in fwd points relative to spot (sssuming that what you mean by r_term is the term interest rate of one currency and r_base the term interest rate of the other). Also, best to ...
• 6,632
Accepted

### Dupire's formula proof

I think you are confused by the definitions and interpretations of $\psi(x,y,z,t)$ and $\phi(x,y,z,t)$. The quantity $\phi(x,y,z,t)$ is a probability density function. Infinitesimally, it represents ...
• 14.7k

### How to price an exchange option using B&S framework?

I think there are 2 ways to get the answer. First way is what Gordon said. But when I first saw his answer, I didn't know why he defined Radon–Nikodym like that, so I thought about it for a long time, ...
Accepted

### How to price an exchange option using B&S framework?

Measure change is still the most natural approach for such problems. We assume that, under the measure $P$, \begin{align*} dX_t &= \mu X_t dt + \sigma X_t dW_t^1,\\ dY_t &= \mu Y_t dt + \...
• 21.2k
Accepted

### Market Value of a CDS

There is a much better pricing formula which is an accurate approximation. Anecdotally I believe that the difference between this and the "offical" CDSW calculator on Bloomberg will be within about 0....
• 2,167

### Formal proof for risk-neutral pricing formula

You have two main papers that show this result: In a finite framework and in a somewhat simplified continuous framework, see Harrison & Pliska (1981), Corollary on page 228, Proposition 2.9 and ...
• 8,119

### Valuation of a swap where both parties can cancel (not settle at market) with accrual method instead of present-value?

I've been thinking about this too and for me, the answer is different from the accrual formula, but may not answer your question ^^'. First little point, maybe your pricing formula is, for the libor ...

### Pricing an open repurchase agreement

There's no such thing as an undated repo. For example , what would happen if the underlying security matures? Term repos of Treasuries of one week to one year are reasonably common. The pricing ...
• 17.2k

• 10.8k
1 vote

### Misconception about replicating portfolio

The 50 value you compute is the payoff of your structure if the underlying is worth 100 at maturity. The initial value is the expected payoff of your trade, then, given the decomposition in call and ...
• 111
1 vote

### How to price a phoenix and snowball type autocallable options?

For anyone who is still interested in this. A snowball can be priced through PDE by using autocallable + doubleNoTouch + doubleOutPut - upOutPut. The solver is easily constructed by playing around ...
1 vote

### Why do we need approximation in option pricing?

We can only get closed-form solutions under certain assumptions about the market dynamics, e.g. in the Black-Scholes framework (share prices follows a GBM), the European option can be valued with the ...
• 1,396
1 vote
Accepted

### Bond and Stock Relationship

Structural credit models like the Merton Model attempt to establish the relationship. However, because the company assets are not trade-able, the delta hedging / no arbitrage assumptions associated ...
• 509
1 vote
Accepted

### CDS protection/contingent leg pricing, taking expectation of interest and hazard rates

After some more trying, I think I have it. \label{eq1} \begin{split} N(1-RR)\ \mathbb{E}\left[ e^{-\int_{t_v}^{\tau}r(s)ds} \mathbb{I}_{\tau<T} \right] & = N(1-RR)\ \mathbb{E}\...
• 137
1 vote
Accepted

### Pricing an open repurchase agreement

This is a bit too general, it really depends of the optionality of the contract : who can break the contract and when ? The repo for a given maturity is just a market parameter, like spot, or ...
• 2,908

Only top scored, non community-wiki answers of a minimum length are eligible