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# 数学代写|期权定价理论代写Option Pricing Theory代考|FINS3635 GRAPHIC ILLUSTRATIONS

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## 数学代写|期权定价理论代写Option Pricing Theory代考|GRAPHIC ILLUSTRATIONS

A variety of response charts was prepared using the standard Black-Scholes pricing model. These charts show how options theoretically respond to the various factors discussed earlier, such as life remaining in the option, volatility, and moneyness.

Response charts are useful for visualizing the impact of various factors on an option’s premium and the related Greeks.

Figure 1-1 depicts the relationship between call option prices, stock prices, and time remaining before expiration. Annotations on the chart delineate the two kinds of value that make up an option’s premium: intrinsic value and time value. Delta is illustrated by the small rectangles drawn on the middle curve. When generating data for Figure 1-1, interest and dividend rates were assumed to be zero, volatility was fixed at $85 \%$, and the strike price was set to $\$ 50$. As shown in Figure 1-1, call option prices almost always rise with increasing stock prices. The one instance where prices do not rise is with an expiring call that is out-of-the-money. An out-of-the-money option with no time remaining has no value. In Figure 1-1, such an option is represented by the lowermost curve when stock prices are less than$\$50$. For stock prices less than $\$ 50$, the lowermost curve lies on the$x$-axis, representing a premium of zero. The same curve shows a premium that increases one-for-one with stock price when stock prices are greater than$\$50$ and the call is in-the-money.

## 数学代写|期权定价理论代写Option Pricing Theory代考|PUT-CALL PARITY, CONVERSIONS,AND REVERSALS

A specific relationship, know as put-call parity, exists between puts and calls of the same strike and expiration. For the sake of simplicity, let us assume that interest rates and dividends are zero. Ignoring interest rates and dividends, the put-call parity relationship can be precisely expressed by the following equation:
$$C-P=U-S$$
In this formula, $C$ is the call price, $P$ is the put price, $U$ is the price of the underlying stock, and $S$ is the strike price of the options. The formula basically says that when both options have the same strike and expiration, the difference between the price of a call and the price of a put must equal the difference between their intrinsic values, and, consequently, that the time value of the call must equal the time value of the put.

## 数学代写期权定价理论代写OPTION PRICING THEORY代 考|PUT-CALL PARITY, CONVERSIONS,AND REVERSALS

$$C-P=U-S$$

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