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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 $...
user107224's user avatar
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}\...
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3 votes
0 answers
160 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 ...
Landscape's user avatar
  • 548
3 votes
0 answers
210 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}\...
Kapes Mate's user avatar
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?
FawaMop's user avatar
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1 vote
0 answers
90 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 ...
BaroqueFreak's user avatar
1 vote
0 answers
85 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 ...
Leoncino's user avatar
  • 161
1 vote
0 answers
92 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, ...
pedro lito's user avatar
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 $...
jthg's user avatar
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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 ...
Jun's user avatar
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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 ...
pinpss's user avatar
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0 votes
1 answer
98 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\...
Alexis Sánchez Tello's user avatar
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87 views

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 \\ ...
StupidMan's user avatar
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118 views

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.
Jonathan Bush's user avatar
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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}_\...
Leoncino's user avatar
  • 161
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0 answers
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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+...
user51121's user avatar
0 votes
0 answers
104 views

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 ...
Anon's user avatar
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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 ...
Sam Palmer's user avatar
-1 votes
1 answer
1k 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 ...
jake_r's user avatar
  • 223
-1 votes
1 answer
207 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)? ...
user12008's user avatar