26
votes
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 ...
- 11.4k
7
votes
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 ...
- 14.5k
6
votes
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 ...
- 2,531
5
votes
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
5
votes
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
5
votes
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 ...
- 5,622
4
votes
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 ...
- 5,662
4
votes
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 ...
- 14.5k
3
votes
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 ...
- 16.5k
3
votes
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 ...
- 16.5k
3
votes
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....
- 2,137
3
votes
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 ...
- 7,959
3
votes
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, ...
- 31
3
votes
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 + \...
- 21k
3
votes
Special Exotic Option Pricing Approach
For homework, I think that people in these forums like when the author explains his current progress/ideas/intuitions.
Try to follow the following steps:
Create a plot with axes: $x=S_T, y=\text{...
- 251
2
votes
Accepted
Pricing of American Deriviatives
For an American option, you have the right to exercise at any intermediate time. Then, at time $T-1$, if you exercise your option, you obtain the payoff $X_{T-1}$. However, if you wait to exercise at ...
- 21k
2
votes
Where to find pricing formulas for affine stochastic volatility jump-diffusion models?
Do these work for you?
P34 of http://web.mit.edu/junpan/www/SVJ.pdf
P1360 of http://www.darrellduffie.com/uploads/pubs/DuffiePanSingleton2000.pdf
P2045 of http://www.math.ku.dk/~rolf/bakshi.pdf
- 4,307
2
votes
Stochastic volatility
The answer is yes. In fact, there always exist a 'Black Scholes like' formula. Easy to show too. If the risk neutral distribution of the price has cumulative density $P$ and probability density $p$, ...
- 4,307
2
votes
Is "interest" positive or negative in the "free cash flow to firm" model?
I would use EBIT*(1-T) instead of [Net Income + Int*(1-T)] (easier to remember), though they are =.
The sign is in fact positive since it provides a tax shield.
Also, the sign is positive b/c ...
- 21
2
votes
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 ...
- 29
2
votes
Are there really closed-form pricing formulas?
There are many types of closed-form expression as you can find in the link here below
https://en.wikipedia.org/wiki/Closed-form_expression#Comparison_of_different_classes_of_expressions
In ...
- 1,009
2
votes
Accepted
Transactional costs for shipping in % based on futures market price
Guess it's all about Rubber Duck Problem Solving. Actually I was working on huge part of old legacy code/formula that misdirect me and I know that I'm probably missing something. But when I form the ...
- 221
2
votes
FX Call under stochastic rates and deterministic volatility
Consider the call option with payoff $(S_T-K)^+$ at the option maturity $T$. Note that the forward exchange rate
\begin{align*}
F(t, T) = S_t \frac{P^f(t, T)}{P^d(t, T)}
\end{align*}
is a martingale ...
- 21k
2
votes
FX futures valuation under negative rates
But the point about neg rates is precisely that you CAN lend and borrow thus. EURIBOR, CHF and JPY LIBOR etc forwards trade >100. So arbitrarily assuming zero rates and thus pricing the forwards at ...
- 5,041
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 ...
- 11
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 ...
- 1,356
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
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 ...
- 2,888
1
vote
How to price a forward struck contract today by changing from a $T>T'$ forward measure to $T'$ forward measure at time $t<T'<T$?
The last step (taking everything outside the expectation ) is invalid. The expression $E[\frac{S_{T'}}{P^{T'}_T}]$ is the expectation of the product of 2 random variables. As such, you need a model ...
- 16.5k
1
vote
Formula for forward price of bond
Some financial terms to begin with:
Dirty Price: It is equal to the sum of clean price and the accrued interest since last coupon payment. Say you hold a semi-annual bond (Purchased on 1st January ...
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