# Questions tagged [payoff]

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### Value of the logcontract $Q^T(t,S)$ with payoff $Q(T,S)=-2lnS_T$

Why is the value of the log-contract (Neuberger ,1990) with payoff $Q(T,S) = -2\ln S$ given by $$Q^T(t,S)=-2e^{-r(T-t)}\left(\ln S + (r-q)(T-t)-\frac{\hat\sigma^2}{2}(T-t)\right)$$ ? It is reported ...
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### Find expected rate of return without drift based on ito process

I would like to know how to solve question (ii), I know it is a cash-or-nothing option but I have no idea how to get the expected rate of return even I use put-call parity. Could anybody guide me I ...
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### Sharpe ratios (and other risk-adjusted metrics) on Terminal wealth (long-horizon payoffs)

I'm exploring financial simulations with bootstrapped returns (TxNBoot) to calculate long-horizon returns. Terminal wealth (e.g compounded returns at T) is a vector of payoffs (NBootx1), typically ...
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### Understanding American option payoff at T+0

The above picture shows the payoff at expiry(in gold) and at current time T+0(in blue) for a bull call spread. I am trying to understand American options and to know if it has any significant ...
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### Shout option payoff replication

I have not seen much talk about exotic options, and if they are actually traded. Is it possible to replicate the payoff of a ‘Shout option’ using standard European/American call and put options?
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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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In the Black-Scholes model, I want to price the so called Butterfly option, where the payoff $P(x)$ is the following function: $P(x)=0$ if $0\leq x\leq 40$, $P(x)=x-40$ for $40\leq x\leq 60$, P(x)=-x+... • 105 0 votes 1 answer 200 views ### Replication of the payoff of a chooser option With numerical examples, how can the payoff of a chooser option be replicated with European call and put options? 0 votes 1 answer 101 views ### YYIIS Inflation swap chapter 16 of Brigo's text Are there errata in the Brigos's text of Interest Rate Models in chapter 16 when it is defined the YYIIS payoff? In formula (16.3) is defined Party A's payoff as: \begin{align} \\ N\psi_i\left[\frac{I\... 3 votes 0 answers 169 views ### Pathwise sensitivities of American options - Derivative of the American payoff function How can I compute the derivative of the payoff function for an American put option? In the paper "Smoking adjoints: fast Monte Carlo Greeks" by Giles and Glasserman (2006) they compare two ... • 558 3 votes 0 answers 226 views ### What is the dynamic of the forward price process under\mathbf{Q}$? Let me define the Spot price process of an underlying as follows: $$dS_{t}=\mu_{S}S_{t}dt+\sigma_{S}S_{t}dW_{t},$$ where$\left(W_{t}\right)_{t\geq0}$is an appropriate Wiener-process, so$\left(S_{t}\...
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Consider a payoff that pays a certain amount N of a vanilla Call (underlying: S, Maturity= T, strike:K). Every semester date Ts before T, if S>K(Ts), then N is increased by 1. This product seems ...
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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 $K$ ...
1 vote
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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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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 $... • 445 2 votes 1 answer 208 views ### Discontinuous derivative payoff approximation Consider a derivative of digital type which pays this kind of payoff at time$T: \begin{align*} g(S_T,k) &= \begin{cases} P_0,~S_T>k \\ S_T, ~S_T\leq k \end{cases} \end{... • 21 0 votes 2 answers 424 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 assetS_T$has a payoff function ... • 157 6 votes 2 answers 840 views ### Architecture of a global pricing library with immutable payoffs By global pricing library I mean a library handling equity, rate etc, hybrid products having several models (BS, LV, SV, LSV) having several numerical methods (analytic formula, MC, PDE FD/FE) I ... • 1,223 1 vote 1 answer 109 views ### Transform of payoff function$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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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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### 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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