Questions tagged [payoff]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0 votes
1 answer
71 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 ...
Mr Frog's user avatar
  • 223
0 votes
0 answers
18 views

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
  • 1
0 votes
0 answers
34 views

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
  • 1
0 votes
1 answer
87 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 ...
FawaMop's user avatar
  • 15
1 vote
0 answers
57 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
  • 15
0 votes
2 answers
103 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 ...
Maurizio Marinaro's user avatar
0 votes
1 answer
144 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+...
Summerday's user avatar
  • 103
0 votes
1 answer
91 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?
FawaMop's user avatar
0 votes
1 answer
78 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
3 votes
0 answers
138 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
  • 558
3 votes
0 answers
161 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
0 votes
1 answer
80 views

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 ...
user25844's user avatar
  • 365
0 votes
0 answers
78 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
  • 180
1 vote
0 answers
83 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
0 votes
0 answers
109 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
1 vote
0 answers
74 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
  • 141
1 vote
0 answers
85 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
0 votes
0 answers
33 views

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
  • 141
4 votes
0 answers
126 views

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
0 votes
0 answers
47 views

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
1 answer
6k views

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 ...
Metrician's user avatar
  • 123
0 votes
0 answers
46 views

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 ...
Metrician's user avatar
  • 123
4 votes
0 answers
167 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}\...
user avatar
0 votes
0 answers
101 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
  • 1
2 votes
1 answer
244 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 $K$ ...
Stelios Kounis's user avatar
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 ...
Aqqqq's user avatar
  • 227
1 vote
2 answers
416 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 ...
Aqqqq's user avatar
  • 227
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 ...
Eka's user avatar
  • 647
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
  • 445
2 votes
1 answer
194 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{...
harvey's user avatar
  • 21
0 votes
2 answers
351 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 ...
ʎpoqou's user avatar
  • 157
6 votes
2 answers
754 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 ...
Olórin's user avatar
  • 1,223
1 vote
1 answer
104 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 $...
Michael's user avatar
  • 21
0 votes
2 answers
367 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), ...
user403033's user avatar
2 votes
1 answer
213 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 ...
chocolatekeyboard's user avatar
0 votes
0 answers
37 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 ...
Sam Palmer's user avatar
0 votes
1 answer
118 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[ ...
stochastic_zeitgeist'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 vote
2 answers
166 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 ...
Elekko's user avatar
  • 427
1 vote
1 answer
124 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 ...
ThePlowKing's user avatar
2 votes
1 answer
149 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 ...
Evan Aad's user avatar
  • 481
-1 votes
1 answer
204 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
0 votes
1 answer
951 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, ...
Lisa Ann's user avatar
  • 2,111
1 vote
2 answers
807 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.
user35777's user avatar