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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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46 views

Convert long/short stock portfolio into one sector ETF position

Assuming a portfolio contains long and short positions in stocks that are in the same sector, is it possible to create a similar overall position using only the sector ETF to which the constituents ...
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1answer
248 views

fx vanilla option's forward delta in single currency

According to Black formula , a vanila fx call option's pricing is $$C(F,\tau) = D[N(d_+)F - N(d_-)K]$$ , where $\tau$ is the time to expiry, $D =e^{-r\tau}$ the discount factor, $F=S/D$ the outright ...
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1answer
61 views

What vol to use when implying strike from delta?

I have a set of implied vols in delta space and want to derive for each delta the corresponding strike. I understand the procedure, but I am not sure what implied vol I should use, whether this has to ...
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1answer
113 views

Volatility scenario generation for value-at-risk

I have the following problem: For a single name plain vanilla equity option calculate 1y VaR for given confidence level. Is there any state-of-the-art or current market practice known on how to ...
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1answer
107 views

Upper bound option price in volatility dimension

All, I have a theoretical question about the value of an option when spot price goes to infinity as a function of volatility going to infinity. I know that for a call option: The option value ...
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42 views

Difference end-of-day price and closing price of option

Is there a difference between end-of-day prices of an option (e.g. Barclays VXX) and the closing price of that option? If so, what is the difference. I cannot find anything clear about this anywhere, ...
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1answer
170 views

SABR PDE spot/forward upper boundary condition implementation

When running my Finite Difference code, I observe something odd. Although implementing a classical (non-reverting) SABR model, I initialized the variables such that it should be equal to Black-...
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1answer
89 views

Pricing an option with sparse data, high underlying volatility and returns

I'm currently pricing American and European options on an underlying with sparse data (interpolated), high annual volatility and returns over the last year around 300%. The product isn't similar to ...
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43 views

Return / yield of an ATM-Call Option on a zero coupon bond

The zero-coupon bond with unit face value and maturity S for a call option with maturity T and strike K is given by: The bond prices $P(t,T)$ and $P(t,S)$ $$\begin{aligned} ZBC(t,T,S,K) = & P(t,S) ...
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62 views

Equity repo close to money market rates?

I've noticed that the repo rate (here I mean the effective financing rate of the forward position in stock) implied from synthetic forwards is almost the same as money market benchmark (XXXibor 3M) ...
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0answers
54 views

American CRR implied vols

Given I have all other parameters lined up with the market (borrow rate, dividends...), if I imply volatility using CRR tree from american call and put with the same strike and expiry, will I always ...
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2answers
87 views

How do you factor in skew when assessing implied volatility for a non-atm option?

If you think volatility is too cheap, how do you decide if an ATM call or an upside call (which trades at lower vol because of skew) is better? Let's say you have a $100 stock. You think the stock ...
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0answers
97 views

Longstaff Schwartz Algrorithm in R

I recently discovered the LSMonteCarlo library in R which basically determines the price of American options via Longstaff Schwartz method. I tried the ...
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0answers
72 views

Intraday option price data European stocks and indices

I am looking for intraday option price data for stocks and indices listed on European markets (SX5E, SMI, DAX, etc). Ideally, I would like to get files as clean as those provided by ivolatility for US ...
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1answer
231 views

derivation of general black-scholes formula

I would like to find a derivation for the Black-Scholes fomrula in the general case (i.e., where the volatility function $\sigma : [0,T] \to \mathbb{R}^+$ and the investment rate $r: [0,T] \to \mathbb{...
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30 views

Trying to understand Strike Adjusted Spread, can someone explain using a simple example?

I should start by saying that I am not a quant, I am someone interested in options but I perhaps lack the mathematics background to always follow along. I recently stumbled upon a terrific article ...
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1answer
74 views

SPX Convexity Spread

In this report on volatility from BNP Paribas, https://globalmarkets.bnpparibas.com/r/Volatility_Express_20171128.pdf?t=BG3REXwMP3NZJRN7wY5Vt&stream=true it states on Page 10 that the SPX ...
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145 views

Skew vs Normalised Skew

In this paper, https://globalmarkets.bnpparibas.com/r/Volatility_Express_20171128.pdf?t=BG3REXwMP3NZJRN7wY5Vt&stream=true, it states that, SPX Implied Normalized Skew: (25D Put IV - 25D Call IV)/(...
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70 views

VIX/SPX Realized Beta Calculation

In https://globalmarkets.bnpparibas.com/r/Volatility_Express_20171128.pdf?t=BG3REXwMP3NZJRN7wY5Vt&stream=true, it states that 3M VIX/SPX realized Beta calculation: Use a blend of 1st, 2nd and 3 ...
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0answers
108 views

SPX/VIX Implied Beta Calculation

In https://globalmarkets.bnpparibas.com/r/Volatility_Express_20171128.pdf?t=BG3REXwMP3NZJRN7wY5Vt&stream=true, it states that 3M VIX/SPX implied Beta = (VIX 3M IVOL*VIX 3M futures)/SPX 3M IVOL ...
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1answer
43 views

Self financing portfolio for a basket of options

How do I create a self financing portfolio consisting of bonds and stocks, for a portfolio of options? My thoughts are that we would need multiple stocks to do so, since the payoff need not be binary,...
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1answer
118 views

Kirk Approximation and Exercise Probability

I have a question about spread options. I'm pricing a put option on two assets, with a strike value of 0: $max(K-(F_1-F_2);0)=max(0-(F_1-F_2);0)=max(F_2-F_1;0)$ I know this kind of options could be ...
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0answers
41 views

Multiple max/min forward start option

I want to calculate the price at $t$ for such payoff at $T$ $$\max(S_T,S_{T_0},C),$$ $$\max\left(S_T,\min(S_{T_0}, C)\right),$$ $$S_T -\min(S_{T_0}, C),$$ $$t<T_0<T.$$ Is there any way or ...
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1answer
175 views

Put pricing embedded in autocall

When pricing an autocall, there are 3 parts: Strip of coupon, Zero coupon bond, Put down and in. Probabilities of a call is given from the trigger level on call dates. However, let's say my ...
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1answer
241 views

Comparing historical to implied volatility

As title states, I am trying to compare historical to implied volatility of a stock. I approximate the single implied volatility (30 days forward) of the stock by first finding 2 series that ...
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1answer
88 views

Quantlib - model changes in option value on day of expiry

I'm trying to model option value changes during the progression of the last trading day before expiry. All option pricing Quantlib examples that I've seen work with day-level granularity. I'm ...
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1answer
76 views

Index implied repo gerater than the stock repo

I've observed that the repo rate implied from options on Euro Stoxx 50 is significantly higher than the repo rate implied from options on individual stocks that are constituents of the index. This is ...
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1answer
83 views

Sigma moves - annualize return or no?

This might be a very simple dumb question. But when you look at a security's annualized volatility over a 3 year period, assuming the security has an annualized vol of 5% and the drawdown over three ...
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0answers
50 views

Options pricing, dividend taxation

I have a question. When pricing, do an equity option, dividend has to be taken into account of course, however since there's a taxation on the dividend does the dividend input has to be cut by the ...
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2answers
78 views

What rate should I passed into Black Scholes to calculate an option price?

I can think of at least two rates with different physical meanings to use. rate on assessed balance. short rate of the underlying stock I understand that BS model is a theory and practice getts ...
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1answer
104 views

Data sources for historical Eurex settlement option prices

I am looking for long history for historical settlement option prices at EUREX. This seems to be more challenge than I could imagine. Eurex themselves doesn't offer that data unfortunately (they only ...
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48 views

Mix a Forward Delta Premium Adjusted and a Forward Delta to construct the volatility surface

I have two brokers who give me delta strategies for USD-COP, but one of them gives me the issue with forward delta, the another one is premium adjusted. Besides, how can I mix them for construct a ...
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1answer
51 views

How might I answer this past exam question relating to the value of a European option under the BMS market model?

The following question, which is not homework, was taken from a past paper for a module I will soon be sitting: Consider a Black-Merton-Scholes stochastic market with drift $\mu = 1$, volatility $\...
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1answer
60 views

How might I answer this past exam question relating to the limiting price of an option?

The following image shows a past exam question that I am attempting to answer (for which I do not have a mark scheme): I believe that under the BMS model, the payoff of a stock at maturity $T$ is ...
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1answer
85 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 ...
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1answer
707 views

What is the importance of alpha, beta, rho in the SABR volatility model?

I just read that SABR model is a stochastic volatility model, which attempts to capture the volatility smile in derivatives markets. The name stands for "stochastic alpha, beta, rho", referring to the ...
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0answers
103 views

American put option in binomial model - arbitrage opportunity?

I'm sorry this must be an elementary question. I spent a good deal of time searching through webs including this site for the problem but I got none. Here's the problem: Say we have a binomial tree ...
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3answers
192 views

How does Rho behaves with moneyness of option?

I was trying to find the relationship between nature of Rho and moneyness of the option. After finding certain values I found that Rho Value keep increases as the option gets further in the money. ...
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1answer
77 views

Using BS Delta to hedge in a LV Model

Why do some people use a Black Scholes Delta instead of the delta given by the Local Volatility model?
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1answer
194 views

Forward Skew in the Local Volatility Model

How does the local volatility model cause a forward skew? How is this different to the skew observed for future tenors in the vol surface?# Also how do LV models underestimate vol of vol?
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45 views

Why is my theta value not realistic in both R?

I'm trying to replicate option pricing in R and am getting very unrealistic values for theta figures. Am I not understanding how theta work? My understanding is theta is the amount an option value ...
2
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1answer
77 views

Implied volatility of inverse quote

Suppose I have a quote of INR/USD and the implied vol surface is also given. Is it theoritically correct to use to same implied vol for analysis of the inverse quote, i.e. USD/INR. Correct me if I am ...
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0answers
51 views

Delta hedge a long option using a short option [closed]

If I long a call option of 1 mio USD/SGD for example, I understand that at strike price (ATM), delta is approximately +0.5. To approximately hedge this delta, I also understand we can short 0.5 mio ...
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0answers
66 views

Different scaling conventions for greeks

I have been following this tutorial (http://gouthamanbalaraman.com/blog/value-options-commodity-futures-black-formula-quantlib-python.html). It says in the conclusion and I quote:It is worth pointing ...
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2answers
49 views

Price and settlement gain calculation in options on an index

The Cboe S&P 500 Index Options - SPX are peculiar in that there is no underlying stock or ETF - they trade the index. I want to make sure that I understand the pricing. On the link above the ...
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0answers
200 views

Derivation of the Pnl of a Delta Hedged Straddle and Risk Reversal

In the link below, in the text it states the following equations: Delta-hedged straddle P&L = Volatility Risk-premium ×| Straddle Vega | and Delta-hedged risk-reversal P&L: ...
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1answer
179 views

Difference in exposure between delta hedged options, ATM straddles and delta hedged straddles

What is the difference in exposures between delta hedged options, ATM straddles and delta hedged straddles. They all seem to provide the same thing, which is exposure to volatility. What are the ...
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2answers
1k views

Gamma Pnl vs Vega Pnl

Why does Gamma Pnl have exposure to realised volatility, but Vega Pnl only has exposure to implied volatility? I am confused as to why gamma pnl is affected (more) by IV and why vega pnl isnt affected ...
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48 views

Pricing call option on S&P 500 [duplicate]

How to price December 2020 maturity European call option of S&P 500 (Strike of 3000). What should be the risk free rate ?
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1answer
42 views

Lower bound for European put option prices — potential contradiction with BS

A classical no-arbitrage argument shows that for a European put with strike $K$ and time to maturity $T$, the price $p$ satisfies $$p \geq \max(0,Ke^{-rT} - S).$$ Is Black-Scholes in contradiction ...