Questions tagged [derivatives]

A financial contract whose payoff is linked to the evolution of an underlying security.

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Should we use the conditional expectation to write the value of an option?

So, I've just started looking into financial mathematics and the following question keeps bugging me. From what I understood, if the market is arbitrage-free and a given contingent claim of value $h$ ...
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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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Difference between closed form binomial option value and monte carlo simulation

I am trying to calculate the price of a European call option using both the the closed form expression and a monte carlo simulation. But the value's I get from both these methods are not the same: ...
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Does settlement method of an instrument affect its payoff?

A stock in foreign market with the fx dynamic (in foreign measure) as the followings: $\begin{align} dS_t &= r_f S_tdt + \sigma_s S_tdW_t^s \\ dF_t& = (r_d-r_f)F_tdt + \sigma_F F_tdW_t^F \\ ...
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Quantlib: VanillaSwap not using underlying Index fixings correctly

I am trying to reperform a vanilla swap. The problem is that the vanilla swap object does not seem to be using the exact fixings of the underlying index. ...
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MBS Dollar roll mechanics

Had a few questions on MBS Dollar rolls: How are dollar rolls affected by Interest rate Volatility? Does the OAS of underlying pools matter to dollar rolls, and if so, how do they affect it? Does the ...
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Modelling forward and correlation dynamics for options on the best-of multiple commodity spreads

I am looking at best-of options on futures (commodities), let's take for example the following payoff specification: $ max(a_{1}-c_{1}, \ a_{2}-c_{1}, \ a_{3}-c_{1}, \ b_{1}-c_{1}, \ b_{2}-c_{1}, \ ...
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What do "heating degree day" prices actually measure?

The futures for Dallas Heating Degree days for July 2022 are trading around 6.83 But Dallas is hot in July and does not typically get any heating degree days So, what does the 6.83 for July 2022 ...
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Book recommendations for derivatives [duplicate]

I would like to ask you, if you could suggest me a good book regarding derivatives. Specifically, i would like a book which is more focused on how the derivatives are working and traded in practise ...
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What is the optimal time for exercising American call and put option?

A 9 month American option (underlying) is known to pay dividend of USD 1 and USD 0.75 at the end of the ...
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How to price an Equity Structured products [closed]

I'm new to equity structured products, I understand the overall construction but I want to have an example of an equity structured product with the steps of creation from seller point view of this ...
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Some thoughts over risk-neutral pricing vs real world expectations

I am trying to connect risk-neutral and physical measure expectations, to understand the difference between a no-arbitrage price and an expected terminal value. Imagine I have a European derivative ...
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When does the underlying become the derivative?

Since options contracts are created by open interest in the contract, it is conceivable that the notional of the total options contracts can exceed the value of the underlying. If that happens, does ...
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I am struggling to prove how when volatility tends to infinity, call option is equal to St and pt option = Ke-r(T-t) [duplicate]

I know how to prove when volatility tends to infinity but i am struggling to prove this. Can anone help?
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How can I hedge basis risk?

Let's say we caught arbitrage between spot and futures, we sold futures and bought spot. The risk-free rate is 5%, and our arbitrage position profit is 5.5%. When the interest rates increase to 6% ...
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Equivalent martingale measure and derivative pricing [duplicate]

So I just recently saw in class that to price a derivative you use what is called an equivalent martingale measure which allows you to compute the price of the contract which then will be the expected ...
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Empirically validating GBM assumptions

I'm trying to get a better grasp on the suitability of Geometric Brownian Motion as a model for asset prices, and I've stumbled across a hurdle which I can't seem to get over. Assuming GBM, the asset ...
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Derivatives of derivatives [closed]

Has financial derivatives of financial derivatives ever been considered in academic or practical settings? Is it useless/useful? Say $C(S_t;K,T)$ is a European call on an underlying $S_t$ with strike $...
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Implied forward rate with forward points

I've been studying the application and derivation of a domestic implicit rate in a FX contract when your input are the forward points and the foreing rate. Let's establish some with some ideas first. ...
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What is the Performance Total Return Swap (TRS)? How about Performance Fixed TRS and Performance Float TRS?

I just know these products recently: Performance Total Return Swap (TRS), Performance Fixed TRS and Performance Float TRS. But cannot find a detailed explanation of the product, all I can find is an ...
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What does a rainfall index-based insurance contract looks like?

I would like to know what a rainfall index-based crop insurance contract looks like. My understanding is like There is pre-agreed index say $I_0$ at time $0$ between an insurance company and a holder,...
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Shock to a system of CDS spread values

Assume we have a system that is built on the CDS spread values. If we want to shock the system, how can we define the shock? For instance, we can define it as the increase in the spread. Of course a ...
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American option under Ornstein-Uhlenbeck stock price

I came across with the following problem: For the Ornstein-Uhlenbeck process $(X_t, 0\leq t\leq T)$ with initial condition $X_0 = x$, find the stopping time $\tau$ that maximizes $\mathbb{E}[e^{-r\...
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Impact on dividend on a autocall

Can someone explain me the impact of the dividends on an autocall structure please ? Is it going to increase the price because of the Short PDI in the structure ?
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Pricing squared derivative: Equating S^2 + a strip of otm calls + a strip of otm puts = only calls

In Peter Carr, Dilip Madan, Towards a Theory of Volatility Trading, 1998, (also derived here by Gordon), both calls and puts are used to replicate any twice differentiable payoff. I suppose one would ...
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Is there anyone trading Then-Current Treasury Forward?

The treasury forward traded for those on-the-run or off-the-run makes sense. You simply trying to hedge the treasury bond already issued by calculating the forward price of the bond. I was wondering ...
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To gamble or not to gamble! (solving a system of ODEs maybe?)

Assume we have some money. At every point in time $0\le t \le T$, we can take either action 1 that is to keep our money until $T$ say in a bank and have an expected return of $f(t)$ or take action 2 ...
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Market Risk - credit v. equity

I am requesting language for the use of derivatives in a portfolio. The goal is to allow the use of derivatives only in instances where the portfolio aggregate market risk exposure (post ...
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Hybrid Derivatives Modelling

Could you please recommend any good books and papers that thoroughly describe the pricing and modelling of Hybrid derivatives? I.e. this question is a "big list" question, the more the ...
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Clarification on how synthetic CDOs work

According to my understanding, synthetic CDOs are essentially credit default swaps (CDS) for a bunch of loans, stored in a special purpose vehicle (SPV). Here, the investor (the one who buys the ...
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How does $(d_2/\sigma) = (1-d_1)$ while deriving the Vanna Formula from BSM? [closed]

Just realized there was a quant finance board, so I figured I'd post it here instead. I'm trying to derive Vanna from the Black-Scholes Model (BSM) equation, but had a hook up on one of the ...
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Discounting power derivatives

My question is whether power/energy derivatives should be discounted or not. I've heard both yes and no from practitioners but I still don't have a strong or clear opinion about it. Derivatives are ...
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Assymetric Rate Distribution

The pandemic has disavowed any notion of nominal rate distributions to being truncated at 0%. However, if Central Banks at Debtor nations are conflicted in that they are incented to suppress interest ...
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Why Do I Need to Scale Options Vega w.r.t T (Time till Expiration)

In the book that I am using, it said that I need scale vega according time with this formula: $\sqrt{90/T}$ to get the weight of the vega w.r.t t. The reasoning it offered is as follows: "...
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Understanding the expected value of the average

I've been looking into Asian Options pricing. Part of the process is about looking for the expected value of the average of a time series undergoing e.g. geometric brownian motion. I came across this ...
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Limit of digital call and put price when volatility goes to infinity

The price a digital call and put in the Black-Scholes model is given by $$c^d = \Phi (d_-), \qquad p^d = \Phi (-d_-), \qquad \text{with} \qquad d_- = \dfrac{\log S_t / K}{\sigma \sqrt{T}} - \dfrac{1}{...
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Risk-neutral pricing to determine no-arbitrage price

We are asked to consider a derivative with payoff $C_t = S_{T}^{1/3}$ at maturity $T > 0$ and to use risk neutral pricing to derve the no-arbitrage price process $C_{t}$. Some context: Let $W$ be a ...
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Value of contingent claim at a given time

Consider a contingent claim whose value at maturity T is given by $\min(S_{T_0}, S_T)$ where $T_0$ is some intermediate time before maturity, $T_0 < T$, and $S_T$ and $S_{T_0}$ are the asset price ...
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Determine Strikes on Option Chain

Does anyone know how to determine option strikes on an option chain are determined for a specific stock? I have been searching online and can't seem to figure out how/why the specific strike are set. ...
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What does M mean in DI Deposit futures contract?

I am trying to understand the forumla for DI1 Brazilian deposit future contract. I am able to figure out everything except M in the following formula: Xt=N×M×(Pt−Pt−1Ft) Lets say if we want to ...
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Seeking criticism of model assumptions

I have been trying to publish a new calculus and options model for seven years. I have been consistently desk rejected, so what I am trying to do is get criticism of my assumptions because they ...
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Do put options experience theta/time decay?

I'm new to quant finance, and I'm confused as to whether or not European put options experience theta decay? It doesn't make sense to me that they should for a couple reasons outlined below, but ...
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Calibrating the mean reversion parameter of the short-rate-model Black-Karasinski

When modelling the term structure of interest rates, one widespread possibility is using the Black-Karasinski(BK) model, which is given by the following stochastic process $$dln\,r=[θ(t)−a\,ln\,r]dt+σ(...
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QuantLib python: CAD IRSwap Conventions [duplicate]

The standard Canadian interest-rate swap convention for the float leg is payment frequency of semi-annual with reset frequency (CDOR3M) of every 3-months. It is not apparent this convention is ...
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Quantlib USDLibor() method

I'm attempting to shift both a discount and projection curve but am having trouble passing through the VanillaSwap() because of the Ibor input requirement -- I'm trying to calculate the dv01 of a US ...
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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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Arithmetic Asian options on two commodities

I am pricing a November-December Asian option on steel via Monte Carlo simulation. I intend to simulate daily prices for the Nov contract from today through end of November, and from today through end ...
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Why should the Discount Curve be risk-free?

I have read up about the discount curve that is being used to value securities. The multi-curve methodology for valuing derivatives was mainly adopted because LIBOR was no longer seen as a proxy for ...
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Reference request (Risk Management + Insurance Theory) [duplicate]

I have to study the following topics: Market and credit risk assessment models Technical risk assessment models: non-life and life Models for the valuation of bonds and for the determination of the ...
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How to trade on whether one asset will be higher than another?

I was wondering if there is any way to trade on whether or not one asset would earn a higher return than another in some predetermined time period. It would be sort of like gambling on horses except ...
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