Questions tagged [derivatives]
A financial contract whose payoff is linked to the evolution of an underlying security.
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Constructing payoff with options
Suppose that COMPANY A has issued a special bond that does not pay any coupons. At maturity T, the bondholder receives the principal (face value) equal to 1,000 plus an additional ...
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Calculating key dates for a Forward Starting Interest Rate Swap versus a Spot IRS
How are the Effective Dates and Maturity Dates of a forward starting IRS (eg: EURIBOR3M 5Y5Y) handled when the forward starting term ends on a non-business day? And if that date is adjusted, how does ...
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Any other ways to hedge a bond portfolio against interest rate risk?
I'm currently taking a (gentle) intro to derivatives class. One of the exercises asked me to discuss duration as a risk measure and to provide alternative methods of hedging a bond portfolio against ...
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Pricing look-back option
I have the monthly price data of a stock starting from December 2020 and I am considering a EU style look-back option issued in December 2020. The payoff at maturity of the look-back option is given ...
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Barrier Reverse Convertible on interest rate
I'm trying to find the price of an barrier reverse convertible on interest rate - https://structuredproducts-ch.leonteq.com/isin/CH1251797945. I have simulated the underlying interest rate by Vasicek ...
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futures exposure targeting (spot vs futures price)
I'm confused over if I should use spot or futures price when targeting a certain exposure. There are many websites that state you should use the contract size * futures price. Other websites, however, ...
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How to convert the parameters of multi-factors cheyette model (quasi-Gaussian model) from tenors to factors?
The book "Interest Rate Modeling" by Andersen and Piterbarg is an extermely fascinating book on interest rate derivatives.
Recently, I have encoutered some issues while reading this book.
...
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Why historical data of futures contract price include data after settlement date of the contracts?
I am studying historical data of futures contract prices. I found there are price data after the settlement date of the contract. For example, for Hang Seng Futures with expiry date of Jun, there are ...
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How are VIX options priced in a mean-reverting framework?
If a trader assumes that the VIX follows a mean-reverting process like the Orstein-Uhlenbeck process, how would they price this non-martingale asset? My intuition tells me a trader would use doob-...
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From parameter risk (sensitivities) to market risk (sensitivities)
In models where the underlying is not modeled directly - such as in the HJM framework or short rate models - how does one then compute the Greeks, i.e. sensitivites wrt. market variables.
As an ...
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Why are we so focused on Zero Coupon Bonds?
In fixed income markets there seem to be two prevailing term structure modelling approaches:
Market Models
HJM Framework
In Market Models, such as the LIBOR Market Model (LMM) and SABR it is common ...
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Analyzing the Impact of S&P Volatility Shift on ATM Straddle Sale: Calculating Loss/Gain[black scholes]
Black scholes:The 1-month implied volatility of S& ;P is 16. The slope of the skewness curve is -1 point per 1%; For example, the 99% exercise trades at a premium of 1 vol point. regarding the ...
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FX FORWARDS Calculating funding cost and wether funding will be expensive or not
Lets say for example my TN for USDHKD point per day spot is -1.9467 and for 1mnth it is -1.4142 and the notional is 100m HKD dollars.
Would you say more or less I would be flat in terms of funding ? ...
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When to use total derivative and when not to?
as I was trying to teach myself financial mathematics, I came across this topic on transforming black scholes pde to a heat equation. I had the exat same question as this post Black Scholes to Heat ...
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Heston model using YUIMA package
I am trying to estimate a Heston model using the Yuima package, but i am in trouble.
This is my script:
...
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Deriving central bank hikes/cuts from a swap curve
Can you please explain the following? Please assume I am 5 years old.
how do you derive the cuts/hikes of the policy rate priced in a swap curve?
why you can derive the cuts/hikes only from a swap ...
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Could a phoenix autocall be priced by a snowball option with zero coupon plus expectation of coupons received in knock out observation dates?
I know that coupons in the phoenix autocall can be received in each observation date if the underlying price in that date does not touch down the knock-in barrier and receiving periodic coupons is ...
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Calculating DV01 for Treasury Futures with CTD switch risk
With rates rising, certain contracts, such as the USZ3, are prone to frequent CTD switches with sometimes large differences in the DV01 of an underlying CTD. Does anyone know of any resources for ...
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Monte Carlo methods: Choosing the best measure
When pricing derivatives using Monte Carlo methods, we take outset in the risk neutral pricing formula which states that we need to calculate the expected value of the discounted cashflows. To do this,...
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Balland - SABR goes normal
To summarise this very long post : please help me understand the undetailed proof of the quoted paper. I am not comfortable using a result I do not fully understand.
I am reading Balland & Tran ...
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Carry for an Interest Rate Swap
I don't get why for calculating the carry of a spot starting swap I need to adjust the difference between the fixed rate and fixing by the Dv01?
For example if I receive in a 5y swap and want to ...
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What is meant by the funding cost of a derivative?
Numerous sources refer to the 'funding cost' of a derivative.
I'm confused as to exactly what cost is being referred to here. To illustrate my confusion, consider purchasing an uncollateralised OTC ...
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Collateral rate vs. funding rate vs. repo rate in derivatives pricing post-GFC
I am reading Funding Beyond Discounting: Collateral Agreements and Derivatives Pricing by V. Piterbarg.
Now I have a question about the relation of the different funding rates in the paper.
$r_C$ is ...
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When to exercise a physical Bermudan swaption
I have seen a lot of literature regarding the valuation of physical Bermudan Swaptions.
However, I could not find any answer to the following question: if you're a trader and an expiry date is ...
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Check for arbitrage - European calls with same strike price, different duration and price
I tried a lot of different things to check for arbitrage on the following calls but didn't succeed.
Let's suppose we have a stock that is currently valued at 40. The interest rate is 0.05 and the ...
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What is the scope of spot lags and spot dates?
In the context of interest rate derivatives, we often speak of the spot date. But of course, there is not a "the" spot date, because there are multiple spot dates, for example for different ...
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Derivatives without analytic expressions? [closed]
I was wondering if there exist options or other derivatives that do not have a known closed-form analytic expression (i.e., some sort of Black-Scholes PDE) and are usually priced using Monte Carlo ...
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future cashflow loan equivalence
I'm trying to improve my understanding of valuation under collateralisation.
One point that is made within multiple sources is for an uncollateralised derivative, how a future cashflow is equivalent ...
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Methods for tracking option open interest intraday
It is my understanding that open interest option values on financial websites are a reflection of a snapshot value each day. Is anyone aware of methods for estimating intraday open interest, or aware ...
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Pricing VIX derivatives using Monte Carlo
I am looking at pricing VIX options and futures using Monte Carlo simulation. Most papers recognise that VIX can be written in terms of the S&P500 index itself, namely as:
$$
VIX_t = \sqrt{-\frac{...
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How to read the notation used for the swap rates in the form 4.412/452 for the 1 year swap rate?
How to read the notation used for the swap rates in Table 20.6 below?
What does 2.412/452 means?
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Predicting Implied Volatility from current and historical volatility
Options implied volatility (IV) and skew can be calculated using the current option prices. I ask to what extent those observed variables are expected to deviate from the "expected" or ...
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What is the intuition behind the VIX formula offset term [duplicate]
In the formula for the VIX we have that the spot value for the VIX is:
The first part of this equation is exactly the formula for the price of a variance swap which is the present value of realized ...
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How does Bloomberg calculate Interest Rate Caps/Floors with Black Scholes Merton Model and Volatility set as "Normal"?
While valuing Interest Rate Caps/Floors in Bloomberg, I saw that we have an option for selecting both Model and Volatility. So, my question is how exactly does Bloomberg value the cap/floor, when we ...
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Monte Carlo Derivative Pricing
In order to try and price some derivatives with payoff $H(S_T).$
I am going to calibrate a few models (BS, Heston and CEV) to some real world data. Then I will calculate option prices as follows:
...
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Estimating the knockout probability of a discretely observed autocall note
For simplicity, let's suppose the underlier follows a Geometric Brownian Motion $S_t\sim\text{GBM}(\mu, \sigma), t\ge 0$ with $S_0=1$. A discretely-observed binary autocall note is a derivative ...
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Is there a way to use normal volatility in the Black–Scholes–Merton model to value interest rate caps? [duplicate]
I am trying to understand if there is a version of the Black–Scholes–Merton model that can use Normal volatilities instead of Lognormal volatilities while valuing interest rate caps and floors?
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How to properly weight fair value, theta, and cega in a multi asset model?
I'm working with a multi-asset worst of model and the outputs are FV,d1,d2,g1,g2,v1,v2,cega, theta.
Its easy to assign proper delta, gamma, vega to the respective asset1 & asset2, but how would ...
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How would I find correlation / association of different time series datapoints with a target variable?
the title is a bit confusing.
Functionally, I have a dataset of N stocks containing options information, short information, and earnings information for each of the N stocks.
For each unique stock in ...
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Sticky Strike vs Sticky Delta - revisited [duplicate]
Given a time series of implied volatility smiles over the last 100 days for a given option (e.g. 1y S&P call, or 1y x 10y swaption), and the corresponding forward rates, what test should be ...
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How do sell-side institutions manage interest rate derivatives books in practice?
I'm interested in real practices of hedging interest rate caps and floors. There are plenty of articles explaining pricing of interest rate derivatives, but not so many explaining hedging such ...
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How to apply a funded equity collar to illiquid stocks?
I investigate a specific case of the funded equity collar [1].
Let's assume that counterparty $A$ already has a stake in share $XYZ$ and wants to get funding out of it from a bank $B$, which does not ...
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Liquidity assessment for OTC derivatives
How does a bank assess the liquidity of OTC derivatives such as swaps, options, and forwards, for which there isn't public data regarding trading volume?
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Derivation of Call Theta from Black Scholes Model [closed]
How is call theta mathematically derived from Black Scholes Model (without approximation) ? Please help me understand each step mathematically.
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Book Recommendations on Options Derivatives [duplicate]
I want to learn about Options Derivatives and am looking for an introductory (as much as possible) book to start with. Any recommendations?
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Price of a simple autocall - Sebastien Bossu Advanced Equity derivatives
I am reading Advanced Equity Derivates by Sebastien Bossu and trying to do the exercises.
In chapter 1 we have the following question :
Consider an exotic option expiring in one, two, or three years ...
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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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Looking for code examples of how to price a worst of (aka multi-asset or minimum of two assets) call/put option
I can find a bunch of phd level formulas for pricing worst of options, but haven't come across anything that translates the math formulas into a programming language.
Are there any known references to ...
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Use of interest rate swaps in liability-driven investing
You probably have home across recent events in the UK bond markets. The Financial Times article "The reason the BoE is buying long gilts: an LDI blow-up" from Sep. 28, 2022 goes through why ...
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