Questions tagged [put]

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2
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65 views

What are the main problems for calculating the implied volatility of in the money American put options?

As stated in the question I have a problem with calculating the implied volatility for in the money put options I have a data set of 2.6 million American style plain-vanilla call and put options. For ...
4
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1answer
116 views

American put option. Exercise time is a random variable, calculation of expected payoff

I got an American put option, where the payoff is $V_\tau = \max(K - X_{\tau}, 0)$ and $X_{\tau}$ is the price of an underlying at the stopping time $\tau < T$. The underlying follows a standard ...
4
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0answers
75 views

Feynman-Kac to derive stochastic representation

$u_t + \frac{1}{2}\sigma^2x^2u_{xx} - \alpha + \lambda((K_d - x)^+ - u) = 0$ with terminal condition $u(T, X) = (K_m - X(T))^+$ $dX = \sigma X(t)dW_t$ $\alpha$ and $\lambda$ are constants Ok so ...
3
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1answer
204 views

Delta Hedging/ Exchange for Currency Options

I'm looking at 2 cases of hedging EURUSD, using call spread or range forward. Lets say spot is 1.1300 and my buy call is at 1.1300 and sell call is at 1.1500. Hypothetically I'm assuming that this is ...
2
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1answer
57 views

is relating bounds to relation between time to maturity and european put option price correct?

J.C. Hull derives the following relation $$Ke^{-rT} - S \le p \le Ke^{-rT}$$ where $p$ is european put option price, $K$ is strike price, $S$ is stock spot price,$r$ rate of interest and $T$ ...
0
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1answer
40 views

Return on Investment for rolled options position on margin [duplicate]

I'm trying to calculate my return on investment (ROI) for an options position on margin that has been rolled. I'll give an example: Sell to Open (STO) a naked put position, for which I collect 100 ...
1
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1answer
889 views

Positive theta on a long put?

I am trying to hand-price options under the Black-Scholes model. Given the following parameters: Stock price: $12.53$ Strike price: $14.00$ Risk-free rate: $0.03$ Annualized Volatility: $0.10$ Time ...
2
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1answer
90 views

Perpetual Put vs European Put

I am looking at a perpetual put option where the strike price is initially the stock price $K(0)=S(0)$ (i.e. at the money), but the strike price grows at the constant risk-free rate $r$ [i.e. $K(t)=S(...
1
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1answer
267 views

Pricing perpetual American put option when interest rate is equal to 0

Let us consider perpetual American put option with interest rate: $r = 0$. The Black-Scholes equation in this case has the form: $$ \frac{1}{2} \sigma^2 S^2 \frac{d^2 V(t, S)}{dS^2} + (r-d)S \frac{dV(...
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0answers
51 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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0answers
114 views

Perpetual American put option with zero interest rate

I want to find an optimal time when we should exercise perpetual American put option. In other words I want to maximize the following equation: $$ V(S) = \sup_{\tau \in \mathcal{\tau}}\mathbb{E}[e^{-...
0
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1answer
299 views

When does the CBOE Put Protection Index (PPUT) make profit?

In my question, as stated in the title, I aim to understand when the strategy of the CBOE Put Protection Index (PPUT) makes profit; particularly during which market conditions. Given the description ...
2
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1answer
291 views

What is The Closed-Form Implied Volatility Estimator (As Defined by Hallerbach 2004) for A Put Option?

"An Improved Estimator For Black-Scholes-Merton Implied Volatility" by Hallerbach (2004) (link to article) provides an equation (Eq. 24, Page 13, and below) for the implied volatility of a call option....
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1answer
600 views

Put call parity in practice

I understand the Wikipedia article for put-call parity on a theoretical level: if you magically had portfolios consisting of 1) long a call, short a put, and 2) long the stock, short a discounted ...
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0answers
63 views

Cox-Ross-Rubinstein - getting volatility

i have exam coming on financial engineering, and need help asap with this thing. Basically there's a European put option ex dividend. We know that the stock price is $S_t = 85$, the exercise price is $...
2
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1answer
2k views

Pricing American Put Options via Binomial Tree in Matlab

I currently am completing a Computational Finance Assignment, and am trying to figure out how to alter this Matlab code which prices a European put or call option, in order to price an American Put ...
1
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1answer
238 views

Finding the replicating portfolio a European T-claim (put)

I have $$dX_0(t) = ρX_0(t)dt ; \qquad X_0(0) = 1\\ dX_1(t) = αX_1(t)dt + βX_1(t)dB(t) ; \qquad X_1(0) = x_1 > 0$$ as the classical Black-Scholes market. I a trying to look for the replicating ...
3
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1answer
751 views

Understanding the relationship between the Black-Scholes formula and a replicating portfolio

I'm self-studying and I'm considering the below example. The specific example is not especially relevant, but I included it for reference. I'm trying to understand the relationship between a ...
2
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3answers
348 views

A paradox about the American Put option price

Suppose a put option on a stock $S(t)$ following a Geometric Brownian motion is given, with strike $K$ and maturity $T$. Let us denote its price at time $t$ by $p(t,S(t))$. Now, by no-arbitrage ...
2
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1answer
695 views

How to create a synthetic put?

I have been reading into Hull's section on portfolio insurance through synthetic puts. My understanding is that in order to replicate a put we should replicate it's delta. Proceeding, Hull states ...
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2answers
104 views

Put Volatility Smiles and Implied Volatility

I have been observing the option chains of put options with differing maturities. I have noticed that those puts with a close expiry date have the steepest volatility smiles. Can someone please ...
1
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1answer
98 views

Put call parity: when are the premiums the same?

Please explain why put call parity could be compared to the payoff of a long forward contract. ie. $C_E-P_E=V_X(0)$ where $C_E,P_E$ are the call/put premiums and $V_X(0)$ is the value of a long ...
0
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1answer
2k views

Use of cash delta vs forward delta and the mirror image rule

There has been no mention in this text of why this formula uses forward delta not cash delta. Why should have this been obvious to the reader? How can a put be delta neutral at 30%, what does this ...
2
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0answers
57 views

Enron - RhythmsNet hedge

I am reading "Power Failure: The Inside Story of The Collapse of Enron" By Mimi Swartz, Sherron Watkins. In the book, the following transaction is described: Enron had USD200mn worth of futures on ...
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1answer
278 views

Payoff of a butterfly c++

I would like to price options (call, put,, butterfly) with monte-carlo method, but actually I need the expression of the butterflay payoff; Could you ^please help me !
1
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0answers
137 views

Volatility Skew for Put and Call options [closed]

Given that the implied volatility follows volatility skew, which one has higher implied volatility? At-the-money put 40 (spot = strike = 40) or at-the-money call 160 (spot = strike = 160)? I am not ...
0
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1answer
112 views

American put option and rising interest rate

Will a rise in interest rate always result in a lower price of an American put option?
2
votes
1answer
282 views

How to hedge a put under the Black-Scholes model?

To hedge a call, one would invest the option price proceeds into $\Delta_t*S_t + B_t = c_t$. (ok) However, a put has negative delta, so I would short $\Delta_t*S_t$ and invest $p_t+\Delta_t*S_t>...
2
votes
4answers
252 views

How to short an option?

It appears to me that retail investors can only buy calls and puts, but not short them through any standardized way (except maybe borrowing the option from a friend ;) ). Is that correct, or how can ...
2
votes
1answer
159 views

The role of Gamma in replicating a put

I am analyzing portfolio protection by replication of a put. Having my portfolio with value $V$ I could buy put giving me the payoff $P$ resulting in a call like pay-off scenario $C=V+P$. Say, I don'...
1
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1answer
46 views

What is the strike of a short put that mimics a covered call

If I am long a stock $X$ which I purchased at $\$100$ and sold a covered call in the front month with strike $\$105$ for $\$2$ then is it true that the covered call is equivalent to a naked put at ...
0
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2answers
51 views

American put on a foreign currency

I know that For an American-style put option, early exercise is a optimal for deep in-the-money options. In this case, it may make sense to exercise the option early in order to obtain the profit ...
2
votes
1answer
114 views

How do I prove that $\lim_{K\searrow0}\frac{P(K,T)}{K} = \mathbb P(S_T=0)$?

I am trying to prove that $$\lim_{K\searrow0}\frac{P(K,T)}{K} = \mathbb P(S_T=0)$$ where $P(K,T)$ denotes the put option price with maturity $T$ and strike $K$ for some stock $S$. Assuming interest ...
7
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1answer
675 views

Why is the Put-Call Symmetry model dependent?

The put-call symmetry states that C(S,t;X,r,q) = P(X,t;S,q,r), and that this works for American options. According to my notes, this is 'model dependent' because it ...