Questions tagged [put-call-parity]

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48 views

Worst-off Options [closed]

I´m working with worst-off options. I´d like to know if I should expect a difference in valuation between WO(call1(S0=100,K=100,vol=20%,rf=0,T=1),call2(S0=100,K=100,vol=20%,rf=0,T=1)) and WO(put1(S0=...
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1answer
72 views

Intuitive explanation of put option pricing based on put-call parity

Assuming no dividends, the put-call parity equation says: $c + \mathrm{Ke}^\mathrm{-rT} = p + S$ where $c$ is the price of the European call, $p$ is the price of the European put, $S$ is the current ...
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0answers
43 views

Put-call parity under a regime-switching model

I need some help. I'm given $J$ different regimes, each one characterized by its own parameters $(r_i, \delta_i,\sigma_i,...)$ with $i\in \mathcal{J}= \{1,2,...,J\}$ ($r$ = risk-free interest rate, $...
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30 views

Why is the correlation that Futures Options have with interest rates opposite to that of the one Stock Options have?

The Put-Call Parity relationship for Stock Options is the following: Call Price - Put Price = Stock Price - Exercise Price + Carrying Costs - Dividends But for Options on Futures where the Options ...
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1answer
95 views
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35 views

The wider bid-ask spread of in-the-forward American option

Why is the bid-ask spread of a in-the-forward/money American call (put) much larger than the out-of-the-forward/money American put (call)? I suppose the answer to the same corresponding question ...
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31 views

Black-Scholes pricing of european call option

I am really confused on the usage of the greeks and the Black-Scholes model for option pricing. To gain some more understanding I am attempting to see if I can price a european call option under the ...
2
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1answer
100 views

Boundary for European Put Option

As an entry level financial engineer, I'm learning about call-put parity, which helps us to get the boundary for call option: $S-Ke^{-rT}\leq c\leq S$, what about put option? Should its upper bound be ...
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3answers
80 views

Equivalent combination of puts

Suppose that a certain stock is currently worth $S_0=\$61$. Consider an investor that buys one call with a strike price equal to $K_1=\$55$, that costs $c_1=\$10$, buys another call with strike price ...
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1answer
81 views

Put-Call parity arbitrage relationship

I would like to know what the relationship is between the time value of call/puts. From the put call parity formula $$C-P = S_{t} - PV(K)$$ and that value of call/put options is simply the sum of ...
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17 views

Insured Portfolio via call + cash: how much cash?

I am unsure about the quantities to keep in the risky asset, S, and the non-risky asset, M, when constructing an insured portfolio via Call + Cash (rather than Stock + Put). My understanding so far is ...
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1answer
105 views

Calculating risk free rates from risky options using put call parity

My questions relates to this post Implying risk-free rates using Put/Call parity , but I am using a different approach. Given: ODAX (Options on "DAX") Settlement prices across different maturities ...
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1answer
157 views

Calculate forward price based on option chain

I've got historical data for a spy option chain which looks as follows ...
1
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1answer
384 views

Proving the put call parity

In my course notes on the put-call parity, the proof is presented by going over two inequalities, namely $\text{RHS} > \text{LHS}$ implies arbtirage and $\text{RHS} < \text{LHS}$ implies ...
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0answers
35 views

What is the effect of put call open Interest on price action

how option put call open Interest affects price actions as put sellers feel price when price goes down or call sellers feel pain when price goes up and how this affects price action. ie when price ...
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2answers
107 views

Why are put and call options worth the same despite that put has no upside whereas call has unlimited upsides?

The following is an interview question. All Black-Scholes assumptions hold. Assume no dividends. Consider a standard European call and a standard European put on the same stock. Assume that each ...
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1answer
66 views

Time to Put or Call a Bond

I was studying putable bond and callable bond on my own, there is an exercise question that was a little confusing to me: I understand what the answer explains, but I am confused that, is a bond "...
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1answer
240 views

Continuous Geometric Asian Options

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 $\sigma$). Let $c(t; ...
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1answer
96 views

How to prove Gamma is the same for a European call and European put with the same inputs?

I saw from a text "From put-call parity, call and put with the same inputs have the same gamma", but I don't see how put-call parity is related to Gamma. Can someone explain? Thanks!
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1answer
207 views

Why is put-call parity defined differently by CME and Wikipedia?

In general, Wikipedia defines Put-Call parity as: C - P = D(F - K) ---------------- C = call price P = put price F = *FORWARD* price K = strike which can be re-...
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1answer
994 views

Build a Synthetic Loan for Personal Finance

Suppose I am short of cash and want a loan for some mundane objective like travelling or buying a car. The interest rate for personal loan with my bank is too high. Is there any way in finance that ...
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0answers
65 views

Prove the following Call and Put relationship: [duplicate]

I need to prove that $$c(S,X,T)=\frac{X}{F}p(S,\frac{F^2}{X},T)$$ where $$F=Se^{(r-q)(T-t)}$$ I am having trouble proving this relationship. Is this relationship even possible? If so, can someone ...
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43 views

Put-call parity for equity share and debt share

Considering Merton's structural approach" for credit risk modeling, we arrive to prove that the pricing formules are $S_t=V_t\phi(d_{T,1})-Fe^{-r(T-t)}\phi(d_{T,2})$ for equity share and $F_t=FP_0(t,T)...
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1answer
65 views

Why do we need to borrow money in the call-put parity? [closed]

As I understand it, the call put parity is given by $$c = p + S - \frac{X}{(1 + r)^T}$$ I understand the rationale behind simultaneously buying the call, put and underlying asset for $S$, but why ...
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232 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 ...
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2answers
239 views

Why do I get a curved line when I plot “implied interest rate” on the strike price?

Currently, I am working on my thesis (MSc. Finance) and I run into an interesting “phenomenon”. I have option data for a non-dividend paying stock. In class I have learned, how to calculate the ...
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0answers
67 views

Is it necessary for $P(K, t) - P(K + s, t) \geq se^{-rt}$ to hold?

Let $P(K, t)$ be a put option with strike price $K$ and expiration time $t$. Let $s > 0$. Is it necessarily true that the inequality $$P(K, t) - P(K + s, t) \geq se^{-rt}$$ holds? I know that ...
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1answer
105 views

How to get Forward price based on Put-Call parity?

Could you advise how to find a forward price using Call/Put (+Spot and Strike) ? Investodepia says that forward is equal to option's strike based on Put-Call Parity but it seems to me there is a ...
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1answer
466 views

Bermudan Swaption

Is there an equation of the kind of call-put parity for Bermudean swaptions ? (maybe an inequality ) Is there an intuitive description of what would be an optimal exercise moment ? Intuitively I ...
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2answers
91 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 ...
2
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1answer
122 views

Determine the maximum arbitrage profit from the given contracts

I really have tough time trying to figure this out. An investor observes the following prices in the market: Euro-Stoxx-Future DEC 148.02-148.03; Euro-Stoxx-Future Call-Option DEC 148.00 1.13-1.15; ...
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211 views

Implied Funding/Borrow Costs in Short-Dated ETF Option Prices

I'm struggling with some anomalous behavior in an analysis I'm running and was hoping for some advice/insights. I'm attempting to extract the implied funding/borrow costs from ETF option prices (say ...
2
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1answer
192 views

Should Put/Call Parity result in Zero Return or the Risk-Free Rate?

Sorry in advance if this is a basic question. I'm examining some potential at-the-money put/call arbitrage. What I found surprised me somewhat: ...
2
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1answer
239 views

Call Option Overvalued and put-call parity [closed]

I have a question regarding if a Call option is overvalued compared to the call price and how you can benefit from the Arbitrage opportunity. My thoughts are as follows: Step 1: Short the call ...
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1answer
122 views

Is there an advantage trading options based on deep in the money Open Interest Volume ratio

Problem: Deep in the money options contracts will be assigned at expiration date. Higher Volume ratio of deep in the money contracts at expiration calls or puts leads to day after expiration date we ...
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1answer
133 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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1answer
166 views

Decreasing value of the Put option with increasing Time to maturity [closed]

Can you think of a situation when increasing the time to maturity lowers the value of a put option? If yes, show the example pls.
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2answers
234 views

Is an options implied dividends DCF model consistent with risk neutral/arbitrage-free valuation?

We're talking about how we price every financial instrument: by discounting the payoff, that is, we take future cash flows and we discount them by a proper rate which takes into account the risk of ...
2
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1answer
174 views

Risk of Put-Call-Parity in practice

When $C+PV(K) \ne P + S_0$, it's an opportunity for risk-free arbitrage (excluding cost). In practice, what potential risk could make the arbitrage fail? I know that failure to build complete ...
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6answers
2k views

Setting the r in put-call parity?

Put-call parity is given by $C + Ke^{-r(T-t)} = P + S$. The variables $C$, $P$ and $S$ are directly observable in the market place. $T-t$ follows by the contract specification. The variable $r$ is ...
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2answers
2k views

Put-call parity for cash settled swaptions

The Euro swaption market is changing from cash to physical settlement quotation in July 2018 $-$ see e.g. "Euro swaptions market prepares for pricign revamp (Risk, 2018)". When describing ...
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3answers
931 views

Put Call Symmetry

I want to show the Put Call Symmetry without using the explicite Black Scholes formula. In other words I want to show Call(t, x, K, T) = Pull(t, K, x, T) where $S_t = x $ for $t \in [0, T]$. I ...
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0answers
70 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
545 views

Understanding put-call parity

I'm a person with math background trying to break into quantitative finance, and there's something about put-call parity that is not making sense to me. Below I'll detail my understanding of the ...
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1answer
390 views

Interpretation and intuition behind the Put-Call symmetry under the Heston Model

I am currently working on a report regarding the put-call symmetry relations under the Heston model. I did all the math and managed to prove the relations using PDE approach. However, I wish to have a ...
2
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1answer
452 views

Question about the vega of a stock

In Black-Scholes model with constant parameters, a call and a put with the same characteristics have the same vega: https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model#The_Greeks Using call-put ...
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0answers
335 views

Convexity of Call option prices using Put-Call parity relationship

I am trying to price vanilla options using a particular Bayesian approach that I have found in a paper. To do that I need to construct a likelihood function, approximating the tail of the distribution ...
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2answers
1k views

Implying risk-free rates using Put/Call parity

I recently purchased SPX options data from the CBOE. Normally, if the data is OK and the Put-Call parity holds, one should expect to correctly imply ZC (Zero Coupon bond) prices and forwards by ...
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1answer
510 views

Violation of the call-put parity

The last price of Wells Fargo (Ticker: WFC) on Thursday, 10/26/17, was $55.62. Options with expiration 11/17/17 had following last prices: Options with expiration 11/17/17 had following last prices: ...
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3answers
6k views

Relationship between forward and option prices

Do forward prices factor into option prices at all? It seems to me from Black-Scholes that you just need a spot price and interest rate r. I understand that $F_t = S_0 e^{r t}$, but I don't know if ...