Questions tagged [pricing]
The pricing tag has no usage guidance.
385 questions
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What does implied volatility say about the underlying?
Here's a question that's been on my mind on-and-off for some time now.
It's well known that Black-Scholes is an unsuitable model for pricing in the current (post 80s) market as it fails to capture the ...
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No expected return in Black Scholes formula: But how about the gamma?
A lot has been written about the fact that the expected return of the underlying asset is not part of the Black Scholes formula. I understand the argument that the performance of the underlying asset ...
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Bond Option: Cash Price or Quoted Price as Underlying
John Hull mentioned in his book using Cash Price(Dirty Price) instead of Quoted Price(Clean Price) in pricing a bond option using Black-Scholes. It confuses me as it seems more natural to assume the ...
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Calibration period
I want to calibrate some model to market data. This could fx be Bates, Kou, Black-Scholes, etc. So, for each model we have a set of parameters which need to be estimated through calibration. Now, my ...
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How to price PIK (paid-in-kind) coupon bond with option by the borrower to pay cash?
I'm trying to price a PIK coupon with an Embedded Option by the borrower to pay in cash. Without the Embedded Option, it is simply a zero-coupon bond paying Principal*(1 + coupon rate)^n at the end.
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What is the minimum price of an option, given no information about Greeks? [closed]
I was asked this interview questions for an analyst level structuring role and it has been bothering me since I can't figure it out:
Assuming the price of an equity is 100, what is the minimum price ...
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486
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Does every process need to be a martingale under martingale measure?
From the pricing theory, processes need to be martingales when divided by the numeraire asset.
A classical example is a stock option:
Consider a money market $B$ being the numeraire asset. When we ...
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Pricing of constant leverage certificates
I am trying to value the open-ended constant leverage certificates like Bull DAX 20x. As the certificates are reset daily with the movements of the underlying asset, how could they be modeled for ...
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Pricing a bond denominated in USD but issued in Europe
I need to price a USD bond using yield-to-maturity from the yield curve (YC). The bond is issued by a German company.
My question is what yield curve should I use: the US Treasury YC or the EUR YC of ...
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796
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Practically, are the prices of 0-strike European calls and stock identical?
By no-arbitrage, the price of a vanilla European call with $K=0$ should be that of the underlying stock (as selling the call is perfectly hedged by buying the stock). However, is this true in practice?...
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Convexity adjustment for futures/FRA under T+D measure
In an internal document in my company, the convexity adjustment for Futures is defined as:
where and P(0,T+D) is the ZC bond maturity at T+D.
I don't understand why is not equal to 1 as I thought ...
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Vanna vs volga and vega
So the bloomberg article that I'm referring to (Bloomberg. Variations on the Vanna-Volga Adjustment. Travis Fisher. Quantitative Research and Development, FX Team. January 26, Version 1) states that ...
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Volga Vanna Pricing Approach
So when using this method to price exotic options , it's stated that we need to calculate the vanna (how vega changes with respect to change in spot prices) of the exotic option and the volga ( how ...
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Convergence of crypto perpetual futures
Perpetual contracts are supposed to track the spot prices through the funding mechanism. Typically, if the future has traded above the spot in the last averaging period used to compute the funding, ...
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Crypto perpetual futures (swaps) pricing away from instantaneous moment of funding
Most perpetual futures offered by crypto exchanges employ a funding payment mechanism, that acts to periodically return the price of the perpetual to the underlying index price. The mechanism is ...
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Tree Pricing FRN Implementation
When pricing a bond via a short rate model on a tree, it seems natural to include intermediate time steps in addition to those corresponding to cashflow dates (i.e. for bonds with American style ...
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What are some interesting recent machine learning related developments in the QF domain?
In 2020 I wrote a MSc thesis on the hedging of exotic options using recurrent neural networks (loosely based on the paper Deep Hedging (2018)by Buehler et al.).
Since then I have been interested in ...
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Why is there a lot of focus on derivatives pricing and much less on stock pricing?
I am a quantitative finance student, and during the first year of this Master’s Degree I couldn’t help but notice that there’s a lot of focus on derivatives pricing and little or none on stock pricing....
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How to fundamentally value cryptocurrencies?
Investing in cryptocurrencies is a wild ride. There is obviously a lot of speculation involved but my question is another one: what are good models to evaluate the fundamental value of ...
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B&S pricing of option with convex transformation
Assuming B&S world, is it possible to price an (European) option on a general transformation $f(\cdot)$ of $X$? What kind of assumptions should we make on $f$? Is convexity sufficient to find some ...
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Pricing Options on Inefficient/Illiquid Assets
I'm currently trying to gather more information on option pricing in very inefficient markets for the underlying. By inefficient, I mean markets with consequential bid-ask spreads (5% or more) and ...
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Does the Lévy characterization imply that the price process of any asset is a Brownian motion?
While studying Brownian motion applied to mathematical finance, I came across these lecture notes by prof Steve Lalley. In the prologue, he gives this explanation for the occurrence of Brownian motion ...
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How should the spread be determined after calculation of expected value?
Suppose I am willing to buy a contract which I believe has a 15% chance to settle to $100 and 0 otherwise. The EV of this contract is therefore 15. How much should I buy this for?
I would answer at ...
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Implication of unique risk neutral measure
I'm reading Shreve Stochastic Calculus II, theorem 5.4.9 (Second fundamental theorem of asset pricing),
This is the part that confuses me :
suppose there is only one risk-neutral measure. This ...
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Implied vs historical volatility in option pricing
I discussed recently with a trader who told me that put options are priced using historical vol, and call are priced using the implied one.
My guess would be that as the put option market is much more ...
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Local Vol vs Stoch Vol Option Pricing
This is an interview question:
Imagine you have a double knock-out barrier option: the current spot is 100, the lower barrier is 80, and upper barrier is 120. The barrier is continuous, meaning that ...
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Pricing for basic option strategies [closed]
If I am trying to price a strategy, say for example a call spread where we are long a call, strike L and short a call strike M, would the pricing formula simply be the Black-Sholes price for the Call ...
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How do market makers calculate bid/ask prices to quote for RFQs, specifically for stocks? [duplicate]
Say a client submits an RFQ to buy/sell 100,000 Apple shares. The market maker will respond with their bid/ask prices.
My question is how are these bid/ask prices calculated by the market maker? Is ...
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Are the buy/sell demand, the underlying spot price and the time value, the only factors in futures contract price?
Are the buy/sell demand on the future contract, the underlying spot price and the time value (days to expiration and the accelerating decay in backwardation or rising in contango, coefficent ) are the ...
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What adjustments need to be made before a Monte-Carlo simulation can be applied for the exotic option $(L_{\text{domestic}}-L_{\text{foreign}})^{+}$
I just want to reassure myself that I understand why Monte-Carlo is the appropriate tool in computing the fair value prices for different options. Let's say we have a Tenor discretization $T_{0}=0<...
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formula for pricing bond-futures
Is anybody able to help me understanding why does $P_t(S)$ appear in the solution to the following problem; deriving the price of bond forward contracts?
Thank you
Given:
$r_t$, the instantaneous ...
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1
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716
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Multi-stage dividend discount model using financial calculator
Instead of the wrote formula approach, this analyst shows that such problems can be decomposed into their cash flows at different points in time, which enables us to use ...
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Why can’t delta’s be used to price double no touch options?
Here is the link to a MATLAB one touch option pricing calculator I used:OT
I tried several inputs and I noticed that the one touch option price is approximately twice the delta of an equivalent ...
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Closed form expression for $\Bbb E(\mathbb{I}_{\{S_{1,T}>S_{2,T}>K \}})$
Is it possible to calculate analytically $\Bbb E(\mathbb{I}_{\{S_{1,T}>S_{2,T}>K \}})$, using the 2-dimensional normal probability function $\Phi_2$, where $S_{1,T}$ and $S_{2,T}$ follow ...
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Option pricing using characteristic function
I'm currently on a mission trying to calculate option prices using the rough Heston model. I've found that this is usually done using the characteristic function of the model, but I must admit that I ...
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Why would one need forward prices to perform derivatives pricing?
I am trying to understand the purpose of inputs the software of my company is using. Amongst others it needs calibration instruments, a model type, initial values of the respective underylings and a ...
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How would I price out and set up a steepening yield curve strategy in which Im long 5yr UST and short 30yr UST futures [closed]
Curious if someone could help me out with pricing this trade idea, or just give me some general tips on a direction I need to head to go about this. I attached a photo if to see how I set up the idea ...
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Pricing interest rate derivatives
In Sec. 3.2 here, Mandel deduces the price $P$ of a derivative on an interest rate $r$ obeys a PDE of the form$$\frac{\partial P}{\partial t}+\frac{1}{2}\beta^{2}\frac{\partial^{2}P}{\partial r^{2}}+\...
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How to price a set of cashflows from which the buyer can choose one?
Lets consider an arbitrage free and complete Model.Let also focus the analysis on the discrete time setting.Assume you have a finite set of random Cashflows $\mathcal{A}$. That means all elements of ...
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1
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Bootstrapping discount and forward curve (using ESRA) and price a vanilla swap
I am just starting to use Quantlib, and want to try and replicate the SWPM-functionality in Bloomberg, and price a vanilla 5Y EUR OIS. Below is the overall swap data used in BBG:
Overall settings
...
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Pricing Dual Currency Bond with Forwards instead of Cross Currency Swap
i got the task to price a bunch of dual currency bonds (EUR/GBP/CHF/USD...) and i am a bit puzzled. As the notional of the bond is in EUR but the repayment is in USD, i assumed that for pricing ...
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Derivation of static replication formula
I know that a way of computing the price of a derivative paying $S^2$ at time $T$ is by making use of the following strategy:
$V=\int_{0}^{\infty} s^2 \frac{\partial^2 C}{\partial K^2}(K=s)ds$
Where $\...
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Is completeness of a financial model relevant for derivatives pricing?
If a market model is complete then every derivative has a unique arbitrage free price. However we are not starting with a model but with a arbitrage free Model class $\mathcal{M}$ (E.g. the ...
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Schedule, Yield-to-Maturity, and NPV of Fixed Rate Bond from QuantLib Python
I would like to price a fixed rate bond using QuantLib Python.
The pricing is fine, however I would like to understand how to extract the Yield-to-Maturity (YTM) of the fixed rate bond, that is, the ...
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Fixed Rate Bond Pricing using QuantLib Python
I have tried to price a fixed rate bond using Python QuantLib and I verified my answer using a DCF model.
Below are my codes for the pricing of the fixed rate bond using Python QuantLib:
...
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Difference arising between Dirty Price and NPV using QuantLib Python
I have used QuantLib Python to price a fixed rate bond.
My codes are as follows:
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Which curves to use for different swaps?
How do we determine which curve to use for pricing different swaps, for e.g. I don't understand how following come:
Interest Rate Swap (USD)
Fixed: USD Treasury
Floating: none
CCS (USDINR)
Fixed: ...
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Pricing of a tracker certificate on basket of index futures
i'm new to Quant Stack Exchange but i already saw that the quality of the answers is outstanding, however, i have a question for which i haven't found an answer yet:
I'm looking for a pricing model/ ...
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What is 450 pips below spot for USD - JPY currency pair?
I'm new to FX derivatives and I'm trying to price a derivative of USD - JPY pair at 450 pips below spot for USD - JPY. Let's assume that the spot is 109.36; would this mean that 450 pips below spot is ...
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What is the way to calculate "Risky PV (Present Value)" (discounting including the probability of default) from bond yield curve?
Instead of using CDS spread to do risky discounting, I would like to use the bond yield curve. Can I directly use the discounting factors from the bond yield curve or do I need to figure out the ...
