IMC (International Market Centers) Quantitative Research OA focuses on mathematics and algorithms. This article shares the latest real questions. oavoservice helps you get the Offer.
📋 Question 1: Option Pricing
Implement the Black-Scholes option pricing model.
import math
from scipy.stats import norm
def black_scholes(S, K, T, r, sigma, option_type='call'):
"""
S: Current stock price
K: Strike price
T: Time to expiration (years)
r: Risk-free interest rate
sigma: Volatility
"""
d1 = (math.log(S / K) + (r + 0.5 * sigma ** 2) * T) / (sigma * math.sqrt(T))
d2 = d1 - sigma * math.sqrt(T)
if option_type == 'call':
price = S * norm.cdf(d1) - K * math.exp(-r * T) * norm.cdf(d2)
else: # put
price = K * math.exp(-r * T) * norm.cdf(-d2) - S * norm.cdf(-d1)
return price
📋 Question 2: Market Microstructure
Implement an Order Book data structure.
from collections import defaultdict
import heapq
class OrderBook:
def __init__(self):
self.bids = [] # Max heap (buy orders)
self.asks = [] # Min heap (sell orders)
self.orders = {}
def add_order(self, order_id, side, price, quantity):
order = {'id': order_id, 'price': price, 'qty': quantity}
self.orders[order_id] = order
if side == 'buy':
heapq.heappush(self.bids, (-price, order_id))
else:
heapq.heappush(self.asks, (price, order_id))
def cancel_order(self, order_id):
if order_id in self.orders:
del self.orders[order_id]
def get_best_bid(self):
while self.bids and self.bids[0][1] not in self.orders:
heapq.heappop(self.bids)
return -self.bids[0][0] if self.bids else None
def get_best_ask(self):
while self.asks and self.asks[0][1] not in self.orders:
heapq.heappop(self.asks)
return self.asks[0][0] if self.asks else None
📋 Question 3: Statistical Arbitrage
Calculate the cointegration relationship between two assets.
import numpy as np
def calculate_cointegration(prices1, prices2):
# Calculate spread
spread = np.array(prices1) - np.array(prices2)
# Calculate mean and standard deviation
mean_spread = np.mean(spread)
std_spread = np.std(spread)
# Z-score
z_scores = (spread - mean_spread) / std_spread
return z_scores
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