Questions tagged [payoff]
The payoff tag has no usage guidance.
39
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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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votes
0
answers
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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 $...
- 609
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0
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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
$$X=\int_{0}^{T}\ln \frac{S_t}{S_0}\mathrm{d}t+\frac{1}{\sigma}\...
user47393
3
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0
answers
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Pathwise sensitivities of American options - Derivative of the American payoff function
How can I compute the derivative of the payoff function for an American put option?
In the paper "Smoking adjoints: fast Monte Carlo Greeks" by Giles and Glasserman (2006) they compare two ...
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What is the dynamic of the forward price process under $\mathbf{Q}$?
Let me define the Spot price process of an underlying as follows: $$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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votes
1
answer
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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{...
- 21
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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 ...
2
votes
1
answer
239
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
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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 ...
- 481
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2
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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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vote
1
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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 $...
- 21
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1
answer
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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 ...
- 227
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2
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778
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.
- 19
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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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2
answers
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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 ...
- 427
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0
answers
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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
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vote
0
answers
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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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0
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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 $...
- 445
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123
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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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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?
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319
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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 ...
- 157
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2
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82
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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 ...
0
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1
answer
127
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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+...
0
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1
answer
80
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Adequate model to payoff
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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117
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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[ ...
0
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1
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948
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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, ...
- 2,111
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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\...
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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 \\ ...
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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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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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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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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 ...
- 233
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2
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364
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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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1
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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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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)?
...
