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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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90 views

Higher Vega with ATM options when Spot is higher

Which would have larger vega, an ATM call option at spot 100 or an ATM call option at spot 200. Apparently the answer is the one with ATM at spot 200. I am not sure how you get this answer. Why ...
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3answers
1k views

Problems with local volatility models (vs stochastic volatility models)

Why is pricing with local volatility models are problem with exotics, mainly due to "the volatility surface is the market's current view of volatility and this will change in the future meaning the ...
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1answer
357 views

Value of Call Option as Volatility goes to Infinity

Why would the value of a call option go infinity as volatility goes to infinity? I understand how you could solve this question by taking $\sigma \rightarrow \infty$ in the solution to the black ...
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0answers
46 views

Different versions of Put-Call Parity

Why is it stated sometimes that $C - P = F$ and in wikipedia it statest that $C - P = D(F-K)$, where D is the discount factor and K is the strike (of both the call and put?). Is this just affected ...
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1answer
339 views

Why is the holder of a basket call long correlation?

I'm told that the holder of a basket call is long correlation. I understand that an increase in correlation leads to an variance of a portfolio. But with one "degree of freedom" (high positive ...
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0answers
455 views

Cashless Exercise of Warrants

This is the formula for a Cashless Exercise of Warrants: X(A-B)/A = Y Where: Y = the number of shares received X = the number of shares purchasable A = price of the stock B = exercise price ...
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0answers
93 views

QuantLib in Python, are there any existing methods to handle the options delta on expiration day?

Tried [ql.Settings.instance().includeReferenceDateEvents = True] and it works for the calculation of NPV using intrinsic value of the option. But Delta is nan for an in-the-money option. I understand ...
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0answers
59 views

Option pricing with negative strikes

I am valuing corporate securities with call option pricing models. In this scenario, it seems possible to have negative strike prices if we assume that some assets or revenues do not have a diffusion ...
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0answers
130 views

What is the vega profile of an up-and-out call option? And why is this important in structuring?

I had this question during an interview but I can't seem to find the answer on the internet.
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1answer
58 views

varswap replication doubt

I have a doubt regarding the varswap replication- I know the portfolio of options with proper weights is a static one, and that there is a dynamic position required in underlying. My confusion is ...
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0answers
543 views

Black-76 Model for Swaption Price and Greeks

I'm in the early stages of developing a swaption pricing model. Suppose $t_1$ is the tenor of the swap rate in years, $F$ is the forward rate of the underlying swap, $X$ is the strke rate of the ...
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0answers
71 views

Calibrating Heston paremeters based on market data for Implied Vol for Call options

Several questions have been asked in here regarding calibration in Heston yet I have not found what I have been looking for, so I will ask: I am looking at a Heston model: $$dS_t=\lambda \sqrt{v_t}...
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0answers
48 views

How to replicate a leveraged dividend stock play

I see that there are some ETNs that use options to replicate a 2x leveraged index, so they pay out double the dividends and track double the returns of the index on a monthly basis. I was wondering ...
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0answers
68 views

Reverse convertible note

When a bank sells a reverse convertible note, what does the bank do in order to generate the pay-off at maturity? Does the bank sell or buy put options? Thanks in advance.
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0answers
51 views

Monte Carlo for constructing the Vol smile in SABR

My purpose is to construct the vol smile using Monte Carlo simulation and not market data. When I search for Monte Carlot methods for SABR I often see the Euler scheme as given for instance in these ...
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0answers
107 views

Delta ATM call with local vol

if we look at the Local Volatility model as briefly described in http://www.emanuelderman.com/writing/entry/the-local-volatility-surface page 13. What is Delta $\Delta$ for ATM call options with in ...
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0answers
183 views

Implied Vol skew VS Local Vol skew (as presented by Derman 1995)

I am reading Derman's article/notes regarding local volatilty: http://www.emanuelderman.com/writing/entry/the-local-volatility-surface. I am examining the graph on page 13. The Implied volatility (...
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1answer
105 views

QuantLib: Unusual point in American option volatility smile

I have a set of American options, for which I got the implied volatility thanks to the package "RQuantLib". I then used splines to interpolate my implied volatility as a function of my strikes. ...
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0answers
74 views

Theta from Black-Scholes PDE - is it possible to use implied volatility?

There is a need to derive theta $\theta$ of an option out of standard Black-Scholes PDE. In usual notation ($P$ - price of an option, $S$ - underlying spot): $\theta=r_dP−Sr_d\delta−\frac{1}{2}\...
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0answers
34 views

Explicit finite difference solution of the diffusion equation

Does anyone know where I could find a numerical example of how the explicit/implicit finite difference methods can be used to evaluate the value of an option for both European and American styles. I ...
1
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1answer
96 views

Do option traders actually have the underlying assets before maturity?

The put and call short, long option graphs don't seem to reflect the fact that a short call or a long put position holder could purchase the assets before maturity especially if that price is below ...
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0answers
79 views

Beta of options based strategy

This is probably a simple/dumb question, but I am not getting it. As per GMO's recent Insight: Second, as can be inferred from Exhibit 1, put writing strategies have a low beta to the equity ...
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0answers
62 views

Calculating Option value with implied volatility

I am trying to solve for the option price given market inputs, but my answer seems wildly off from the price mentioned in the market. As an example, I use the SPY index option here: https://finance....
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0answers
304 views

Pricing options using a binomial tree

The past few months, I have been taking the financial engineering course offered by Columbia. It is a great course but there is a huge disconnect between the theory they teach and the questions then ...
4
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2answers
579 views

Interpertation of delta hedge error in Black Scholes

I have spent some time to prove the delta hedge error as described in this paper paper page 16-17 by Davis. The proof is discussed here Deriving Delta Hedge error in the B-S setup (part 2) (a post by ...
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0answers
118 views

CIR calibration error (Python)

No joy on Stack Overflow, perhaps more fitting here. I have a script which includes a calibration of the CIR model for short rates, the entire script and dependencies are at: https://github.com/...
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1answer
857 views

Bachelier model VS Black Scholes in call option pricing. Why are they so different?

I have been working with Bachelier model for some days but when I experimented with the model I saw some unwanted result with huge differences from the Black Scholes model. Bachelier model is ...
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1answer
152 views

Deriving Delta Hedge error in the B-S setup (part 2)

In this paper paper page 16-19 by Davis and this discussion derivation of the hedging error in a black scholes setup, the derivation of the delta hedging error in the Black Scholes model is discussed. ...
2
votes
1answer
58 views

Change in call price Value as time goes by

In various papers and discussions in here I have seen that in delta hedging setup people compute the Change in value/Price of Call option by: $$ dC_t = \Theta_t dt + \Delta_t dS + \frac{1}{2} \...
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0answers
117 views

Stop loss strategy using options

I normally trade stocks using Robinhood, and use a simple stop loss strategy for 2:1 P/L trades. I recently got invited to use their options via their phone app, and was interested in trading some ...
3
votes
1answer
91 views

Wrong proof that call price is concave function of strike price

I've somehow proved that European call price $C(K)$ is a concave function of strike price $K$, but I can't spot where the mistake is. Suppose $K_1 < K_2 < K_3$ and thus $K_2 = \lambda K_1 + (1 -...
4
votes
1answer
127 views

European Call price for an asset with mean reverting (Vasicek model) dynamics

Let's look at a stock with a mean reverting price dynamics: $$dS_t = a(S-S_0)dt + \sigma dW_t$$ If we let $\sigma=0.25$ and $a=-0.5$ then the variance of this process is: $$Var(S_t) = 0.199\sim0.2$$ ...
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0answers
66 views

Structured Energy Option Pricing

Let's say I have an option with the following terms. This is for an energy product (ie natural gas) The contract will last for 6 months The payoff is the difference between the first of month index ...
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1answer
93 views

VaR of long options

I just had a chat with a risk manager who thinks that the daily VaR of a long option with a maturity under three months should be 'Premium of the Option' / 20 (assuming twenty days in a month) ...
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1answer
258 views

Bachelier model call: computation of delta of a call option

The price of a call with a stock with Bachellier process as its underlying and zero interest rate is giving by: $$C(t)=(S(t)-K)\Phi(\frac{S(t)-K}{\sigma \sqrt{T-t}})+\sigma \sqrt{T-t} \phi(\frac{S(t)-...
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1answer
52 views

Is this the correct shape of Cox-Ross-Rubinstein's recombining binomial tree?

Most texts display the binomial tree like this: However when I run my calculation the tree in reality looks like this: Does this look correct to you? I am using these standard formulas: $$u=e^{\...
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1answer
247 views

Call option with underlying following a Bachelier process

I am trying to reach a derivation/proof for how to price a call option when its underlying asset follows a Bachelier process with unknown drift term: $$dS_t=...dt+\sigma dW_t$$ but zero interest ...
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2answers
53 views

IvyDB: St as the only unknown variable in the BS formula

Good afternoon. I have a dataset of options (IvyDB), with the price of the options, and all the information needed to retreive the price from the Black-Scholes formula. All except the price of the ...
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2answers
231 views

Contingent claim and Derivative

What's the difference between a derivative and a contingent claim? What is an example of a derivative which isn't a contingent claim? Since options or swaps are examples of derivatives that are ...
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0answers
63 views

Arbitrage opportunity with call options? [duplicate]

Call options with strikes 100, 120, and 130 on the same underlying asset and with the same maturity are trading for 8, 5, and 3, respectively (there is no bid-ask spread). Is there an arbitrage ...
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0answers
39 views

Sub-Optimal exercise

I have seen exercise multiples applied to account for sub-optimal exercise of American style options in the case of employee share schemes (as the employees are irrational). I would like to know if ...
2
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0answers
90 views

American options — doing better than Black's approximation when $r = 0$

I am trying to find the implied volatility smile for an American call option with a known dividend during the option tenor. For the sake of argument, let's say today is Jan 1, the dividend $D$ is paid ...
1
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1answer
132 views

Using return on equity instead of risk free rate when pricing an equity call option

I am currently a second year university student studying business, so excuse my lack of knowledge regarding the subject. I am currently studying the binomial options pricing model, which involves ...
4
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3answers
945 views

Black Scholes and high dividend paying stocks

I understood there were 3 alternative methods of dealing with dividends in BS: 1) using a continuous dividend yield as an input; or 2) setting dividends to zero and subtracting the PV of divs from the ...
2
votes
0answers
71 views

Barrier Option with Time-Dependent Rebate

Is there a closed form solution for American Single-Barrier Options (specifically Down-and-Out Calls) which undergo linear principal amortization based on the amount of time passed before being KO'ed? ...
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0answers
36 views

Low estimator when valuing american option using Broadie and Glassermann Monte Carlo tree with antithetic branching (R)

I've been looking into Monte Carlo methods for valuing american options. Now, I found an R code by Stefano M. Iacus that values the option using a tree (based on Broadie and Glassermann) without use ...
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0answers
101 views

Static Replication of a Barrier at a single observation time

I have an instrument that looks like this: On expiration $T$, it is a down and in put At a specific time $t<T$ before expiration, if the underlying is above a barrier $B$, the whole option becomes ...
4
votes
1answer
610 views

Why is there a difference in American option prices when comparing pricing methods (Python)?

I have written a Python script to price American options using Least Squares Monte Carlo and added a QuantLib implementation below (analytical/binomial/finite difference) to compare. The problem is ...
2
votes
1answer
126 views

Settlement of VIX derivatives

Currently reading the paper of John M. Griffin and Amin Shams "Manipulation in the VIX?". My questions has to do with settlement of VIX derivatives (options and futures on VIX). The paper states that ...
2
votes
2answers
168 views

Flaw in the following argument with Binary Options and Skew

A Binary option is ATM and expires tomorrow. If the skew of the vanilla options steepens (left side up, right side down) what happens to the price of the Binary Option. I know that using a ...