Questions tagged [pricing-formulae]
The pricing-formulae tag has no usage guidance.
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Calculate the amount of shares of a deposit without converting to numeraire
Let F a mutual fund with two assets A and B. Initially, F contains 1 unit of A, 1 unit of B, and there is 1 share allocated to Alice. At a later time, Bob deposits 2 units of A into F. How can I ...
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Special Exotic Option Pricing Approach [closed]
I am currently stuck with the following problem:
You need to price the following exotic option, where the share price of Stock ABC is the underlying:
• Time to maturity: 2 years
• Right to exercise: ...
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Interesting finding... "Adjusted Kirk's" and "Bjerksund-Stensland" are exactly the same ??? Spread option calculation
This is more of an academic question. The results are SO close, I think they are ACTUALLY THE SAME FORMULAS. So someone published a paper with a "new" method to adjust Kirk's formula to ...
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Pricing of LIBOR based CF settled after the LIBOR fixing by switching from risk-neutral to forward-neutral measures
When deriving the LIBOR-based swap rate formula in any interest rate model, expressions of the following types appear naturally:
Literature tells us that, switching to the – forward neutral measure, ...
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Pricing formula under a new risk-neutral pricing measure:
From the fundamental asset pricing theorem, we know that in the absence of arbitrage opportunities, the present value of an asset paying $\Psi(X)$ at maturity time $T$ is given by:
\begin{equation}
...
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How to calculate the theoretical price of a forward in CHF on a stock index future in EUR?
I am looking for a pricing model of the following contract, which is basically a forward contract, maturity in 3 month with some sort of strike on a (equally weighted basket of) stock index futures in ...
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How is calculated the futures/forward convexity adjustment for FX?
I could find lots of stuff online for IR derivatives but it seems there isn't too much on FX for this specific adjustment.
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Pricing of forwards contracts
Of the courses I am taking in college this semester, two are Financial Mathematics and Derivatives. In each course, we learn different formulas to calculate the forward price of a forward contract. ...
user52981
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Misconception about replicating portfolio [closed]
I am solving a problem in which following payoff is provided:
With $S_0=100$ and $T=8$. Looking at the payoff it seems obvious that it is replicated with two european put options ($K=100$ and $K=150$)...
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FX futures valuation under negative rates
Market participants use negative interbank rates (LIBOR JPY/CHF) for the valuation of FX futures. Does this make any economic sense?
Positive rates in valuation formula indicate opportunity cost of ...
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Are there really closed-form pricing formulas? [closed]
Good morning to all,
I wanted to post this question here hoping to have more details.
The concern, in my opinion, comes from the fact that the concept of "closed-form" is not clear. Because, ...
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Is the pricing formula for FX Forwards the same for FX Swaps?
If I use fwd_price = S*(1+r_term)/(1+r_base) to determine the theoretical value of a forward, how should I tweak the formula to price a FX swap? Assuming swap = fwd-spot, swap_price = S*(1+r_term)/(1+...
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Forward contract on a given financial product $P$
I would like to know whether my reasoning is correct or not.
Let $\pi_t$ be the price of a financial product $P$.
The forward associated to a forward contract on $P$ that settles at time $T$ is given ...
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FX Call under stochastic rates and deterministic volatility
Lets denote $S_t$, $r^d_t$,$r^f_t$ respectively the FX spot, the domestic rate and the foreign rate at time $t$.
Lets $\mathbb{Q}^d$ , $\mathbb{Q}^f$ respectively be the domestic and foreign mesures,...
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How to price a phoenix and snowball type autocallable options?
I'm currently studying the pricing of autocallable options, especially snowball (accumalated coupon) and phoenix (accumlated coupon, but the coupon may also be autocalled if the underlying price ...
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Transactional costs for shipping in % based on futures market price
Real case: Imagine I want to move an oil from one terminal to another.
I have about 20 +/- tanker companies, but all of them have max capacity on their top deadweight (DWCC) vessel about ...
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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 ...
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Bond and Stock Relationship
Is there any formulair relationship between the price of a corporate bond and the stock on the same company?
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How is this steel price implied based on enterprise value-to-Ebitda?
How was the steel price of $650 per ton calculated based on the forward-looking enterprise value-to-Ebitda in this Bloomberg news article?
https://www.bloomberg.com/news/articles/2018-03-23/tariff-...
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Barrier Option with Time-Dependent Rebate
Is there a closed form solution for American Single-Barrier Options (specifically Down-and-Out Calls) which undergo linear principal amortization based on the amount of time passed before being KO'ed?
...
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Bond prices tend to 100 at maturity?
Let's assume we have a fixed-income bond, which is paying a yearly coupon. For example a 3 year bond, 1% fixed coupon, issued at par. So we have
at issue ->
$Price=\frac{1}{(1+0,01)^1}+\frac{1}{(1+0,...
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CDS protection/contingent leg pricing, taking expectation of interest and hazard rates
The Pricing and Risk Management of Credit Default Swaps, with a Focus on the ISDA Model
Screenshot: Pricing protection leg of a CDS, by OpenGamma
In the screenshot above, I am having trouble ...
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Pricing an open repurchase agreement
I am wondering, how do you price a open-ended repo (when a maturity date is not set)?
I have done some research and have found no formula's or even an explanation of how to value such a repo. In ...
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Is "interest" positive or negative in the "free cash flow to firm" model?
FCFF = net income + non-cash charges + interest x (1 - tax rate) - long-term investments - investments in working capital
My intuition is: if the company is receiving interests payments, then the ...
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Valuation of a swap where both parties can cancel (not settle at market) with accrual method instead of present-value?
Consider a single-name total return swap (TRS) on some reference asset $S$. For concreteness, suppose the length of the contract is one year with quarterly resets, and the performance of $S$ is ...
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How to price a forward struck contract today by changing from a $T>T'$ forward measure to $T'$ forward measure at time $t<T'<T$?
Suppose that the payoff of some contract is $V_{T}=S_{T}-S_{T'}$ where $T'<T$ and we want to value the contract at time $t<T'$ (the situation where this arises could be a total return swap, ...
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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 ...
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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 ...
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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 ...
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Stochastic volatility
Suppose we have :
$\frac{dS_{t}}{S_{t}}= \sigma dW_{t}$ with $\sigma_{t}$ a stochastic volatility process.
How to compute $\mathbb{E}^{Q}[(S_{T}-K)+]$ ? Is there a BS alike formula : "$S_{0}N(d+)-Ke^{-...
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Pricing of American Deriviatives
Reading the book by Andrea Pascucci "PDE and Martingale Method in Option Pricing" I am struggling with a very simple issue. Suppose we want to find the price of an American derivative $X$ in an ...
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Where to find pricing formulas for affine stochastic volatility jump-diffusion models?
Does anyone know a reference where I can find the pricing formulas for vanilla calls in the affine stochastic volatility jump diffusion class of models such as SVJ and SVJJ?
I am looking for ...
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What are the technical events that fluctuate quoted asset (e.g. forex) prices? How does it relate to the purchase of currency contracts?
This is a generic question about the quotations of assets but for the sake of reducing ambiguity, let's consider the EUR/USD exchange rate. If the answer varies for other asset classes, please note ...
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Implication of the Greeks under jump diffusion model
Consider jump diffusion model proposed by Merton and Kou.
As far as i know, most paper only dealt the valuation of option under the jump diffusion model.
As i expected, because of the ...
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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 ...
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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-...
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Is stock price priced in the uncertainty?
Consider a one step binomial tree model for stock price. The classical setup is as below:
At time $t=0$, the stock price is $S_0$.
At time $t=1$, the stock has probability $p$ to jump up to price $...
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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-...
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Question on an approximation in pricing formula
I am reading the book An Introduction to Financial Option Valuation. The following on page 58 makes me confused:
For the formula:
$\exp \left\{ -1.96\sigma \sqrt{t}+(\mu-0.5 \sigma^2)t \right\}$,
...
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How to price an exchange option using B&S framework?
Consider a market composed by two stocks whose prices $X$ and $Y$ are given by B&S diffusion:
$$dX_t= \mu X_t dt+ \sigma X_tdW_t$$
$$dY_t= \mu Y_t dt+ \sigma Y_tdB_t$$
Supposing the market is ...
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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 $- ...
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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, ...
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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-...
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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 ...
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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?
...
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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 ...
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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 ...
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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 ...
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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 ...
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