Questions tagged [payoff]

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65 views

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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1answer
117 views

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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2answers
187 views

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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1answer
269 views

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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0answers
36 views

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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1answer
95 views

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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2answers
73 views

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 ...
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0answers
126 views

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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1answer
75 views

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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2answers
203 views

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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1answer
120 views

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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0answers
30 views

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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1answer
104 views

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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1answer
691 views

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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2answers
114 views

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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1answer
106 views

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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1answer
140 views

“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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1answer
153 views

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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1answer
736 views

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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2answers
543 views

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.