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Questions tagged [options]

A contract that gives the owner the right, but not the obligation, to buy or sell a security at a fixed price in the future.

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3
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2answers
119 views

Deriving implied volatility programmatically

I'm working on a project to calculate the value of options using Python. I'm using the Black-Scholes model, and I can get accurate results by plugging in a given ...
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0answers
34 views

Effective gamma/vega hedging

I want an options position where I can short some options to pocket the premiums and benefit from the time decay. I also want to be vega and gamma neutral. Is there an established way to find which ...
-5
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0answers
26 views

Renassiance fund [on hold]

Was the success of the Renaissance fund genuine? Or did they simply pile everything into mortgage backed securities and everyone withdrew in 08 because they were using it like a bank?
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1answer
76 views

How many options would be required to dynamically replicate the VIX nowadays?

The VIX is a portfolio of OTM options on the SPX with non-zero quotes. From CBOE white-paper: Only SPX options quoted with non-zero bid prices are used in the VIX Index calculation. [...] As ...
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0answers
38 views

How to hedge payments in a foreign currency?

I´m confronted with solving the following exercise: "Suppose that now is 1 March. You are a UK based exporter who´ll export products to a U.S. company for 250,000 US dollars and to a French company ...
2
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0answers
58 views

Black-Scholes equation Variational / Weak form

I am having difficulty deriving the weak formulation of the Black-Scholes Equation. I have multiplied it with a test function phi and integrated over Omega. But results on the internet suggest ...
0
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1answer
56 views

Cox-Ingersoll-Ross Zero Bond Put Option

according to Brigo & Mercurio (2006): But how is the Zero bond Put of the CIR model? I couldn't find any information about that. Thanks in advance. Regards Chris
0
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0answers
21 views

0 Delta on Forward starting Equity basket option

I wanted to confirm the inherent reasoning behind 0 delta on a weighted equity basket option. For instance, if we have a basket option with a forward starting initial fixing date, we can expect the ...
1
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1answer
55 views

Variance of a spread for options on spreads

I was reading the paper: https://people.umass.edu/nkapadia/docs/Negative_Vega.pdf In the equation $(5)$, he is defining the variance of the spread as: $$\sigma_1^2S_1^2 + \sigma_2^2S_2^2 - 2\...
5
votes
2answers
416 views

Numeric example to understand the effect of option gamma

Gamma of an option is the second partial derivative of the theoretical value of an option wrt the underlying. It should be the rate of change of Delta wrt to a small change on the underlying. However ...
2
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0answers
119 views

Bimodal option pricing based on P.D.F

is there any literature on option pricing given the pdf of the underlying asset - e.g. i am interested in seeing how prices for a range of strikes ought to compare based on, say, a simple normal ...
1
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1answer
128 views

Simulating assets of different currencies

I have a situation as follows: One year call option on a Euro stock with a Euro denominated strike. Knock in feature as follows - The option can only pay out if the growth in the Euro stock over ...
0
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0answers
37 views

Hedging option delta

Let's say I am long 1000 50 delta call options. I need to hedge my deltas now. There can be infinite ways to do this. How should I think about proceeding wit this? My first thought was, if the ...
0
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2answers
104 views

Proving a process is martingale under the Risk Neutral Measure

Show that for any $\lambda \in \Re$, the process $Y_{\lambda,t}$ defined as: $$Y_{\lambda,t} = (S_t/S_0)^\lambda e^{-(r\lambda-\lambda(1-\lambda)\sigma^2/2)t}$$ is a martingale under the risk ...
1
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0answers
56 views

Proving an Expectation

Assume the risk-free bond $B_t$ and the stock $S_t$ follow the dynamics of the Black & Scholes model without dividends. Consider the perpetual American put option with payoff $(K-S_\tau)^+$ when ...
2
votes
1answer
42 views

theta for SPX options vs. E-mini future options

Interactive Brokers currently shows the following data for SPX options at strike 3000 and expiry 2020-09-17: calls: bid/ask 234.10/236.30, theta -0.362 puts: bid/ask 146.70/148.40, theta -0.225 Then ...
4
votes
1answer
337 views

Numerical simulation of Heston model

I am trying to simulate on Python random paths for a general asset price as described by the Heston model: \begin{equation} \begin{aligned} dS_t &= \mu S_t dt + \sqrt{\nu_t} S_t dW^S_t \\ d\nu_t &...
2
votes
1answer
142 views

Floating Strike Lookback Call Option

Assume the risk-free bond $B_t$ and the stock $S_t$ follow the dynamics of the Black & Scholes model without dividends (with interest rate $r$, stock drift $\mu$ and volatility $\sigma$). If $r=\...
0
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0answers
86 views

cashflow for floorlet option on 1 month Libor under Vasicek

I have to figure out the cashflow for a floorlet option written on 1 month Libor under Vasicek model by considering yield curve power series expression and bond pricing equation: Has anyone an idea ...
3
votes
2answers
503 views

Finding price of the power option

Let's assume a market with $d=1$ and $X=X^1$ satisfying $dX_t=\sigma X_t\,dW_t,\: \: X_0=1,$ where $(W_t)$ is a standard Brownian motion. Assume that $\mathbb{F}$ is the natural filtration of $X$ ...
5
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0answers
374 views

Calculating dealer gamma imbalance/exposure for an options strip

Have seen this being done for years (primarily by J.P. Morgan and a couple other bank research desks) and am attempting to re-create for my own personal research. I’ve read the forums on here but no ...
1
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0answers
26 views

Option Bounds in a risk-averse incomplete market

I was reading the article "On option pricing bounds" by Ritchken(1985). It uses linear programming to determine options upper and lower bounds. Given a single period model, the stock price will have ...
1
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2answers
88 views

Instantaneous change in value of portfolio

I am trying to figure out an intuitive explanation for the instantaneous change for the value of a portfolio (essentially I'm creating a self-financing portfolio to replicate a derivative payoff). ...
4
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2answers
263 views

Best topics to begin Quantitative Finance Research/Programming

I have a background in mathematics (Functional Analysis and Probability Theory) and am looking to acquaint myself with research in quantitative finance, particularly with a programming component. ...
9
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3answers
16k views

How to replicate a digital call option

Call Option S=100 K=100 Payoff=1 (option is not available) How can i replicate this (payoff) with calls and puts with strike prices with multiples of 5$ Thanks for help
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0answers
47 views

Equity option demand and supply

Some academic studies have documented that market makers short index option and long equity option on net. It is easy to understand that Non market makers want to buy index option because of their ...
0
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0answers
50 views

construction of 25 delta butterfly

Could anyone explain why the 25-delta butterfly strategy is constructed by 0.5*(25-delta call + 25-delta put) - ATM straddle? Especially, what the term "25-delta" represents in "25-delta butterfly ...
5
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4answers
8k views

Derivation of the formulas for the values of European asset-or-nothing and cash-or-nothing options

The asset-or-nothing European option pays at t = T the value of the stock when at time T that value exceeds or is equal to the exercise price E, and nothing if the value of the stock is below E. So, ...
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0answers
49 views

Why does the price of a butterfly spread increase are rate exponential [closed]

I know that stock prices are assumed to be Stochastic processes that follow Geometric brownian motion. The expectation of stock prices at time T given stock price at time 0 is: $e^{-rT}S_0$. However, ...
1
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1answer
69 views

Which currency to hedge a position in FX options?

Let's assume a bank sells to a client a put of \$1,000,000 dollars on USDJPY at 110 in 6 months. The delta of this put is -0.6, spot is 112. So to hedge its position the bank has to short \$600,000 ...
2
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0answers
36 views

Replicating portfolio with stock, bond and call option

I am trying to interpret: I am having trouble interpreting the replicating strategy: Context: $\phi$ is a generic payoff function, 0 < S < $\infty$, assumed throughout to be twice ...
1
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0answers
19 views

Hedging a long position-one period from Steven Shreve Stochastic Calculus for Finance

The following question is taken from Steven Shreve Volume 1, Chapter 1, Exercise $1.6$ (Hedging a long position-one period) Consider a one period binomial stock model with $S_0=4$, $S_1(H)=8$ and $...
17
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3answers
9k views

What causes the call and put volatility surface to differ?

I currently have a local volatility model that uses the standard Black Scholes assumptions. When calculating the volatility surface, what causes the difference between the call volatility surface, ...
2
votes
1answer
72 views

Are vega vanna volga methods/models used in equity derivatives or only in FX and why?

Vega vanna volga models seem to be popular is the FX derivatives market and are often calibrated via 25 delta risk reversal, vega weighted butterfly, and ATM straddle quotes. I am wondering if they ...
0
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0answers
27 views

Reading this ichimoku cloud how do you read this wdfc chart?

Having trouble reading the charts as the breakouts aren’t clear What do you see in this chart?
2
votes
1answer
111 views

Problem of stochastic differential equation (SDE)

Please help to answer this stochastic differential equation (SDE). Thank you very much.
2
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0answers
21 views

Data sources for historical ICE settlement option prices, volume & open interest

I am looking for long history for historical settlement option prices, volume & open interest at ICE Europe (specifically fixed income). This seems to be more challenge than I could imagine. ICE ...
2
votes
1answer
161 views

For which would you expect the liquidity on instrument X to be the greatest: its spot, future, option or swap?

Would like $X$ to remain general, but if needed, let's say GBPUSD Exchange Rate. By liquidity I mean overal market volume across exchanges / ease of opening and closing positions / total notional ...
2
votes
0answers
20 views

Implying a required rate of return on an option from the required rate of return on the underlying

Is it possible to imply a required rate of return on an option from a required rate of return on the underlying? For example, given a known cost of equity, can you calculate the required rate of ...
1
vote
0answers
35 views

Log Contracts on Equities

Are log contracts on (e.g) equities traded a lot in the market? I have seen that a lot of it is described for volatility modelling in bergomi's book. what is the liquidity of such options?
4
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1answer
253 views

Options basics needs to be cleared

I'm not clear for the terminology of options and the mechanics of it. Any help is appreciated. For example the following statement: European call option of Apple stock with maturity 1 year and ...
4
votes
1answer
164 views

Why do options market makers make their spread as wide as the corresponding vega?

I've heard that option market makers make their bid ask spread as wide as the vega of the contract they are quoting. If the quoted spread is narrower than the vega of the option it is said that the ...
8
votes
2answers
4k views

Pricing of a Foreign Exchange Vanilla Option

To understand how Bloomberg prices foreign exchange vanilla options , I extract the following screenshot from its OVML function. The Black-Scholes formua for vanilla options are \begin{split} & P=...
9
votes
5answers
28k views

Why do some people claim the delta of an ATM call option is 0.5?

I am looking for a mathematical proof in terms of differentiating the BS equation to calculate Delta and then prove it that ATM delta is equal to 0.5. I have seen many books quoting delta of ATM call ...
2
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0answers
30 views

CVA for options

I am trying to do a simple unilateral CVA for call and put options. I found this discretised formula online: $$ CVA = \sum_{i=1}^m \frac{EE(t_{i-1})DF(t_{i-1}) + EE(t_i)DF(t_i)}{2} \left( PD(t_i) - PD(...
2
votes
0answers
51 views

Delta Hedging Example

I was reading Dynamic Hedging by N. Taleb and in the chapter dedicated to the delta, there is this example of a trader position in options (one-month European call, flat yield curve, forward is ...
1
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1answer
36 views

some questions about pricing an asset or nothing put option with a strike price equal to St

I am working on a homework exercise where the aim is to price an asset or nothing put with K = St, offcourse the normal formula could be used St * N(-d1), but I was wondering if pricing the asset by ...
1
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0answers
50 views

FX option trading [duplicate]

Are all trades quoted in implied vol terms delta neutral trades? If trades are not delta neutral at the initiation does that mean it is speculative trading? Why/ why not?
0
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0answers
44 views

Strictly increasing asset price under a risk-neutral probability measure?

I am reading a paper on option pricing under jump processes in continuous time. There is a section labeled examples where the authors work under a risk neutral probability measure and derive option ...
3
votes
0answers
65 views

Pricing of future options

I have the following question on futures options: There is a Black’s model, which is a variant of the Black-Scholes formula that is used to price stock options. The Black’s model prices future ...