# Questions tagged [payoff]

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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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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 $... • 609 4 votes 0 answers 168 views ### Black-Scholes market and payoff with integrals I am struggling with the following exercise: Prove that on Black-Scholes market, with some parameters$r, \mu, \sigma >0, a payoff $$X=\int_{0}^{T}\ln \frac{S_t}{S_0}\mathrm{d}t+\frac{1}{\sigma}\... 3 votes 0 answers 169 views ### Pathwise sensitivities of American options - Derivative of the American payoff function How can I compute the derivative of the payoff function for an American put option? In the paper "Smoking adjoints: fast Monte Carlo Greeks" by Giles and Glasserman (2006) they compare two ... • 558 3 votes 0 answers 224 views ### What is the dynamic of the forward price process under \mathbf{Q}? Let me define the Spot price process of an underlying as follows:$$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}\... • 239 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 2 votes 1 answer 220 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 ... 2 votes 1 answer 248 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 ... 2 votes 1 answer 150 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 ... • 481 1 vote 2 answers 443 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 ... • 237 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 ... • 21 1 vote 1 answer 3k 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 ... • 237 1 vote 2 answers 832 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. 1 vote 1 answer 2k 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 ... • 657 1 vote 2 answers 170 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 ... • 427 1 vote 0 answers 60 views ### 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? • 15 1 vote 0 answers 93 views ### 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 ... • 151 1 vote 0 answers 89 views ### 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 ... • 161 1 vote 0 answers 94 views ### 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, ... 1 vote 0 answers 57 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 ... • 445 1 vote 1 answer 129 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 ... • 243 0 votes 1 answer 195 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 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 asset S_T has a payoff function ... • 157 0 votes 1 answer 78 views ### 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)$? It is reported ... • 263 0 votes 1 answer 100 views ### Understanding American option payoff at T+0 The above picture shows the payoff at expiry(in gold) and at current time T+0(in blue) for a bull call spread. I am trying to understand American options and to know if it has any significant ... • 15 0 votes 2 answers 147 views ### Constructing payoff with options Suppose that COMPANY A has issued a special bond that does not pay any coupons. At maturity T, the bondholder receives the principal (face value) equal to 1,000 plus an additional ... 0 votes 1 answer 153 views ### How can I price this option? [closed] In the Black-Scholes model, I want to price the so called Butterfly option, where the payoff$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+...
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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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### 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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### 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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### 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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### 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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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), ...
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 ...