Questions tagged [payoff]

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Pricing any Payoff structure using Binomial Tree(Pricing DDTPS)

I just wanted to confirm if its theoretically possible to value any derivative with a payoff that can be replicated by a portfolio of options,underlying and bonds. I wanted to value DDTPS which is a ...
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How to apply the Spanning Formula (Carr-Madan) on European Call-option?

In the paper Optimal positioning in derivative securities (Carr & Madan, 2000) the so-called "Spanning Formula" for replicating payoffs is presented in section 2.1 as equation (1). It ...
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How to combine compound calls and puts such as to have a guaranteed fixed payoff at expiration?

Let there be 2 European vanilla options: Call; Put; Both options expire at time T2 > T1 > t=0. We also have 4 additional options available to us: Compound call on call; Compound call on put; ...
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Why is the parity graph in Natenberg shifted up?

In chapter 4 of Natenberg's "Option and Volatility and pricing", he discusses how to draw parity graphs for option positions. These are defined as a plot of the intrinsic value of the ...
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Swap Fly PnL Payoff Question

Stuck on this payoff question. What is the PnL on 5s10s30s on a swap fly 10k 01, where the fly moves 8 to 26bp? Any ideas would be much appreciated.
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Calculating CDO pay-off

Background I got a model for the distance-to-default of an instution in a system of banks from the paper "An SPDE model for systemic risk with endogeneous contagion". Therein they postulated ...
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Why should a seller of autocall (down out ones) cover gamma risk?

I wonder why sellers of Autocalls should cover the gamma ? The autocall I'm talking about is of this type : While the spot never goes below 70 % of the initial value, nothing happens. If it happens, ...
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Measurability of contingent claim in State-variable approach

I'd like to know, if we have the filtrations $\mathbb{F}$ and $\mathbb{G}$ with $\mathcal{F}_t\subset\mathcal{G}_t\subset \mathcal{F}_t\vee \sigma(\eta)$, for $\eta$ being independent of $\mathcal{F}_\...
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Pricing of strange Asian lookback option with European-style payoff $\max\{ \max_{u\in[0,T]}S_u-\frac1T\sqrt{\int_0^TS_t^2\mathrm{d}t},0\}$

I am trying to price the Asian lookback option at time $t$ with time-$T$ (European) payoff $\max\{M_T-A_T,0\}$, where $$M_t=\max_{u\in[0,t]}S_u,\quad A_t=\frac1t\sqrt{\int_0^tS_u^2\mathrm{d}u},$$ and $...
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Prices and returns

I want to convert the payoff of an Asian and a lookback Call option with prices in their corresponding with returns. Example: for an European Call $\varphi(S_T)=(S_T-K)^+$, so knowing that $S_T=S_0(1+...
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What's the difference between a normal Autocall and a Phoenix Autocall?

I understand the structure of the autocall, how they're priced and their contingent coupons. What I'm not completely clear on is the difference between a "vanilla" Autocall and a Phoenix ...
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Is there a general method by which we can replicate a given payoff? [duplicate]

I've been studying how to replicate different payoffs using options and zero-coupon bonds, and each time there's a different approach to solving the problem. I've been wondering if there's a general ...
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Black-Scholes market and payoff with integrals

I am struggling with the following exercise: Prove that on Black-Scholes market, with some parameters $r, \mu, \sigma >0$, a payoff $$X=\int_{0}^{T}\ln \frac{S_t}{S_0}\mathrm{d}t+\frac{1}{\sigma}\...
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What is a lookback rate put option

I've come across an option called a look-back rate put option. However, the source I got this from did not say what this is. I understand what a look-back put option is, but the rate bit is throwing ...
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What is the probability of a lookback option ending in the money (CRR-model)

I would like to compute the probability that a certain lookback option ends in the money, let's say that the option has the following payoff $h_N=\max\left\{0,K-\min\{S_1,...,S_N\}\right\} $ where $K$ ...
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What does "first-order effect" mean?

In the textbook Asset Pricing by John Cochrane, on p. 25, it says: "This prediction holds even if the payoff $x$ is highly volatile and investors are highly risk averse. The reason is simple: if you ...
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What does it mean by "A one period bond is a claim to a unit payoff." from Cochrane?

In the textbook Asset Pricing by John Cochrane, on p. 19 (corresponding table on p. 18), he claims that A one period bond is of course a claim to a unit payoff." What does he mean by "a unit ...
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How do we calculate option payoff before expiration?

I am trying to simulate a bull spread option and I have used an online tutorial to calculate payoff at expiry but I am having difficulty simulating the payoff ...
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Wheres is this method/notation of option portfolio payoff design from?

The "desired position" in the image is a set of slopes $(0,1,-1,0)$, and a set of strike prices between these slopes $\mathbf{K}=(98,100,102)$. The payoff is then designed by finding the positions $...
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Discontinuous derivative payoff approximation

Consider a derivative of digital type which pays this kind of payoff at time $T$: \begin{align*} g(S_T,k) &= \begin{cases} P_0,~S_T>k \\ S_T, ~S_T\leq k \end{cases} \end{...
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Construct a portfolio of European call options with a certain payoff function

My question is similar to Replicate a Portfolio with Given Payoff but I am not quite sure how to apply this to my problem. A portfolio of European call options on an asset $S_T$ has a payoff function ...
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6 votes
2 answers
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Architecture of a global pricing library with immutable payoffs

By global pricing library I mean a library handling equity, rate etc, hybrid products having several models (BS, LV, SV, LSV) having several numerical methods (analytic formula, MC, PDE FD/FE) I ...
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Transform of payoff function $w_c=(\sqrt{y}-K)^+$ [closed]

I am working on a project where I price EU call options written on the VIX index. The payoff function of interest looks like $w_c=(\sqrt{y}-K)^+$ where K is the strike price and y is the value of $...
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Seagull Spread payoffs

I'm looking at different option strategies and the ways that their payoffs differ (and therefore how they can differently be used). I'm looking at the long seagull (buy a call spread and sell a put), ...
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2 votes
1 answer
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Explaining an Option product: SIX Discount Certificates

So I have the option with the important info above. I am trying to generate a portfolio that represents the option. However I am stuck on the first hurdle as I believe it is a call option as the ...
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Transform the payoff to be non-zero

Is there any way to transform the basic call option payoff $V(s,0) = \max(s-K,0)$ such that $g(V(s,0))\neq 0$ $\forall s $, where $g()$ is the transform function of the payoff. This is to use in a ...
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Get expected joint-payoff price of digital options from individual payoffs

I am trying to model a joint distribution $f(X_1,X_2)$ (where $X_1$ and $X_2$ are market prices of the options) and then find from it the value of joint payoff price: $F(X_1, X_2; B_1, B_2) = E[ ...
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1 answer
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Swaption Corridor Payoff Diagram

What does the payoff diagram look like for a long payer swaption corridor? For example, suppose that I am looking at a long-payer $1 \times 10$-year swaption with 10Y swaps as the underlying. If I ...
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Finding optimal drift, importance sampling, least square monte carlo

I am working with Importance sampling for Least Squared monte carlo and have now problems understanding the implementation of the Robbins-Monro algorithm for finding the optimal drift for finding ...
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Differentiating a Payoff

Okay this is probably going to be an extremely easy/straightforward question but I thought I should post it here just to double check. Suppose I have a payoff $\Phi = (S_{T}-K)^{+}$. Now let's say I ...
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2 votes
1 answer
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"For any random variable $X$, someone will be willing to buy and someone to sell a financial instrument, whose final payoff is $X$."

we will assume that for any random variable $X:\Omega\rightarrow\mathbb{R}$, some investor will be willing to buy and some investor will be willing to sell a 'financial instrument' whose final payoff ...
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conservative approach payoff table

With the conservative approach, we choose the decision which maximises minimum payoff. I was wondering which decision is chosen if 2 decisions have equal minimum payoff (which is the maximum)? ...
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Expected payoff and weighted average price

Settings Let you're trading a security whose probability to be equal to $S_{T}$ at time $T$ follows a p.d.f. like the ones in the picture below. (That is just an example found with Google images, ...
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How is holding an European call option equivalent to holding an asset-or-nothing call option and writing a cash-or-nothing call option?

The cash-or-nothing call option has a payoff that is equal to the strike price. All three options have the same expiry date.
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