## It’s the end where I begin

If you get the reference of the title without googling it, apir! Hahaha. Wala lang. đ

The topic about matrices made an impact on me. Kasi, at its core, it’s a simple concept. Pero yung mga applications niya, WAGAS. Hahaha. Very useful even in real life situations. đ

Hmm.Â IfÂ I were to describe this class in a sentence, it would be, “This class really is really numerical.”

I’m not sure if having no MPs as a requirement is a good thing, or a bad thing because throughout the sem, this course got me thinking, “Pano kaya i-poprogram itong mga inaaral namin. Haha. And how to actually optimize the programming solutions.” :))

To my (legit) classmates (1-2:30 PM),

Thank you for being a sport whenever we play a game in class. Hahaha.
Sa mga naging classmate ko pag nagsisit in sa ibang class time, thank you for letting me sit on your supposed chair. Hehe. đ

Au revoir, mes amis! đ

## J4: Fourier Transform in Option Pricing

Fourier Transform (FT) option pricing is a standardÂ option pricing method. But what is an option?

An option is a financial derivative that represents a contract sold by one party (the option writer) to another party (the option holder). The contract offers the buyer the right, but not the obligation, to buy (call) or sell (put) a security or other financial asset at an agreed-upon price (the strike price) during a certain period of time or on a specific date (exercise date).

Generally, thereÂ are two kinds of options. A Call Option and a Put Option.

Call options give the option to buy at certain price, so the buyer would want the stock to go up. Conversely, the option writer needs to provide the underlying shares in the event that the stock’s market price exceeds the strike due to the contractual obligation. An option writer who sells a call option believes that the underlying stock’s price will drop relative to the option’s strike price during the life of the option, as that is how he will reap maximum profit.

This is exactly the opposite outlook of the option buyer. The buyer believes that the underlying stock will rise; if this happens, the buyer will be able to acquire the stock for a lower price and then sell it for a profit. However, if the underlying stock does not close above the strike price on the expiration date, the option buyer would lose the premium paid for the call option.

Put options give the option to sell at a certain price, so the buyer would want the stock to go down. The opposite is true for put option writers. For example, a put option buyer is bearish on the underlying stock and believes its market price will fall below the specified strike price on or before a specified date. On the other hand, an option writer who shorts a put option believes the underlying stock’s price will increase about a specified price on or before the expiration date.

If the underlying stock’s price closes above the specified strike price on the expiration date, the put option writer’s maximum profit is achieved. Conversely, a put option holder would only benefit from a fall in the underlying stock’s price below the strike price. If the underlying stock’s price falls below the strike price, the put option writer is obligated to purchase shares of the underlying stock at the strike price. [1]

OneÂ advantage of FT option pricing is its generality in the sense that the only thing necessary for FT option pricing is a characteristic function of the log terminal stock price. This generality of FT option pricing speeds up the calibration and Monte Carlo simulation with various exponential LĂ©vy models. [2]

References:

[1] http://www.investopedia.com/terms/o/option.asp . May 5, 2017
[2] Matsuda, Kazuhisa . Introduction to Option Pricing with Fourier Transform: Option Pricing with Exponential LĂ©vy Models.

## J2: Vector Gaming

In what other ways can we use vectors? Give one sample applicationÂ andÂ describe/illustrate how the vector can be used.

We can use vectors to illustrate possible movements in games. See picture of the chessboard below. Hehe.

If anyone wants to play Chess, I’m g! :DD

## J3: Cognitive Symmetry

A useful application of symmetry can also be found in a lot of things relating to group theory.

One of these things is the status quo bias. It is the tendency of an individual especially when in a group, to like things to stay relatively the same so as to avoid conflict to arise. [1]

In this certain case, symmetry can be a good or a bad thing. The status quo bias is good to the extent that it helps avoid conflicts to arise, but at the same time, it may hinder innovation.

References:
Kahneman, D.; Knetsch, J. L.; Thaler, R. H. (1991). “Anomalies: The Endowment Effect, Loss Aversion, and Status Quo Bias”. Journal of Economic Perspectives. 5 (1): 193â206. doi:10.1257/jep.5.1.193.

## J1: Yo-Yo Ma

Yo I’m Bernadette Misa. You can call me Berna, Misa o kaya bernablues hahaha :))

What were your thoughts when you enrolled in this course?

When I enrolled in this course, I was kinda scared kasi ito yung isa sa mga subjectsÂ na nagkukunwaring CS subject pero Math course Â naman talaga hahah. Sabi pa nga nila, Math 56 daw to. Hahaha. Pero when I learned thatÂ si Sir Paul yung maghahandle, nagkaroon ako ng pag-asa na baka pwede namang mahalin ang subject na ito. Hehe. :))

How comfortable are you with math?

Math is my waterloo hahahu. Math ang dahilan kung bakit hindi Engineering course yung pinili ko nung UPCAT :))

Whatâs your dominant feeling right now?

Gutom as always hahaha. Also, excited for the pizza parties to come! Hahha (Hi Sir! :)) )

• #### Paul Rossener 4:59 pm on February 22, 2017 Permalink | Reply

Pizza party, yay!

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